[{"data":1,"prerenderedAt":2575},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung":546,"formula-related-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung":2565},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":65,"checks":2499,"conditions":2527,"conditionsHtml":2528,"deprecated":2529,"description":2493,"extension":2530,"figure":2529,"figureCaption":2529,"figureHtml":2529,"formulaId":2531,"latex":2532,"latexHtml":2533,"level":2534,"meta":2535,"navigation":2536,"path":2537,"redirectFrom":2538,"related":2539,"seo":2543,"stem":2544,"subject":582,"summary":2545,"tags":2546,"variables":2551,"__hash__":2564},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung.md","Primfaktorzerlegung",[550,551,552,553,554],"Primfaktoren","Primfaktorzerlegung berechnen","Zahl in Primfaktoren zerlegen","Primzahlzerlegung","Faktorbaum",{"type":556,"value":557,"toc":2492},"minimark",[558,563,801,833,836,849,852,856,889,1376,1408,1706,1838,2115,2119],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571,572,617,618,767,768,796,797,800],"p",{},"Eine ",[568,569,570],"strong",{},"Primzahl"," ist eine natürliche Zahl, die genau zwei Teiler hat: ",[573,574,577,599],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,595],"semantics",{},[589,590,591],"mrow",{},[592,593,594],"mn",{},"1",[596,597,594],"annotation",{"encoding":598},"application\u002Fx-tex",[573,600,604],{"className":601,"ariaHidden":603},[602],"katex-html","true",[573,605,608,613],{"className":606},[607],"base",[573,609],{"className":610,"style":612},[611],"strut","height:0.6444em;",[573,614,594],{"className":615},[616],"mord"," und sich selbst. Die ersten Primzahlen sind ",[573,619,621,678],{"className":620},[576],[573,622,624],{"className":623},[580],[582,625,626],{"xmlns":584},[586,627,628,675],{},[589,629,630,633,637,640,642,645,647,650,652,655,657,660,662,665,667,670,672],{},[592,631,632],{},"2",[634,635,636],"mo",{"separator":603},",",[592,638,639],{},"3",[634,641,636],{"separator":603},[592,643,644],{},"5",[634,646,636],{"separator":603},[592,648,649],{},"7",[634,651,636],{"separator":603},[592,653,654],{},"11",[634,656,636],{"separator":603},[592,658,659],{},"13",[634,661,636],{"separator":603},[592,663,664],{},"17",[634,666,636],{"separator":603},[592,668,669],{},"19",[634,671,636],{"separator":603},[634,673,674],{},"…",[596,676,677],{"encoding":598},"2, 3, 5, 7, 11, 13, 17, 19, \\ldots",[573,679,681],{"className":680,"ariaHidden":603},[602],[573,682,684,688,691,695,700,703,706,709,712,715,718,721,724,727,730,733,736,739,742,745,748,751,754,757,760,763],{"className":683},[607],[573,685],{"className":686,"style":687},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,689,632],{"className":690},[616],[573,692,636],{"className":693},[694],"mpunct",[573,696],{"className":697,"style":699},[698],"mspace","margin-right:0.1667em;",[573,701,639],{"className":702},[616],[573,704,636],{"className":705},[694],[573,707],{"className":708,"style":699},[698],[573,710,644],{"className":711},[616],[573,713,636],{"className":714},[694],[573,716],{"className":717,"style":699},[698],[573,719,649],{"className":720},[616],[573,722,636],{"className":723},[694],[573,725],{"className":726,"style":699},[698],[573,728,654],{"className":729},[616],[573,731,636],{"className":732},[694],[573,734],{"className":735,"style":699},[698],[573,737,659],{"className":738},[616],[573,740,636],{"className":741},[694],[573,743],{"className":744,"style":699},[698],[573,746,664],{"className":747},[616],[573,749,636],{"className":750},[694],[573,752],{"className":753,"style":699},[698],[573,755,669],{"className":756},[616],[573,758,636],{"className":759},[694],[573,761],{"className":762,"style":699},[698],[573,764,674],{"className":765},[766],"minner"," Die ",[573,769,771,784],{"className":770},[576],[573,772,774],{"className":773},[580],[582,775,776],{"xmlns":584},[586,777,778,782],{},[589,779,780],{},[592,781,594],{},[596,783,594],{"encoding":598},[573,785,787],{"className":786,"ariaHidden":603},[602],[573,788,790,793],{"className":789},[607],[573,791],{"className":792,"style":612},[611],[573,794,594],{"className":795},[616]," ist ",[568,798,799],{},"keine"," Primzahl.",[564,802,803,804,832],{},"Jede natürliche Zahl ab ",[573,805,807,820],{"className":806},[576],[573,808,810],{"className":809},[580],[582,811,812],{"xmlns":584},[586,813,814,818],{},[589,815,816],{},[592,817,632],{},[596,819,632],{"encoding":598},[573,821,823],{"className":822,"ariaHidden":603},[602],[573,824,826,829],{"className":825},[607],[573,827],{"className":828,"style":612},[611],[573,830,632],{"className":831},[616]," ist entweder selbst eine Primzahl oder ein Produkt aus Primzahlen. Diese Zerlegung ist eindeutig: Bis auf die Reihenfolge gibt es nur eine. Gleiche Faktoren fasst man zu Potenzen zusammen.",[564,834,835],{},"So geht man vor:",[837,838,839,843,846],"ol",{},[840,841,842],"li",{},"Die Zahl durch die kleinste Primzahl teilen, die sie ohne Rest teilt.",[840,844,845],{},"Mit dem Ergebnis genauso weitermachen.",[840,847,848],{},"Aufhören, wenn das Ergebnis selbst eine Primzahl ist.",[564,850,851],{},"Die Primfaktorzerlegung hilft beim Kürzen von Brüchen und beim Finden von ggT und kgV.",[559,853,855],{"id":854},"beispiele","Beispiele",[564,857,858,859,888],{},"Zerlegung von ",[573,860,862,876],{"className":861},[576],[573,863,865],{"className":864},[580],[582,866,867],{"xmlns":584},[586,868,869,874],{},[589,870,871],{},[592,872,873],{},"360",[596,875,873],{"encoding":598},[573,877,879],{"className":878,"ariaHidden":603},[602],[573,880,882,885],{"className":881},[607],[573,883],{"className":884,"style":612},[611],[573,886,873],{"className":887},[616]," durch fortgesetztes Teilen:",[573,890,893],{"className":891},[892],"katex-display",[573,894,896,992],{"className":895},[576],[573,897,899],{"className":898},[580],[582,900,902],{"xmlns":584,"display":901},"block",[586,903,904,989],{},[589,905,906,908,927,930,942,945,957,960,972,975,987],{},[592,907,873],{},[909,910,911,915],"mover",{},[634,912,914],{"stretchy":603,"minsize":913},"3.0em","→",[916,917,920],"mpadded",{"width":918,"lspace":919},"+0.6em","0.3em",[589,921,922,925],{},[634,923,924],{},":",[592,926,632],{},[592,928,929],{},"180",[909,931,932,934],{},[634,933,914],{"stretchy":603,"minsize":913},[916,935,936],{"width":918,"lspace":919},[589,937,938,940],{},[634,939,924],{},[592,941,632],{},[592,943,944],{},"90",[909,946,947,949],{},[634,948,914],{"stretchy":603,"minsize":913},[916,950,951],{"width":918,"lspace":919},[589,952,953,955],{},[634,954,924],{},[592,956,632],{},[592,958,959],{},"45",[909,961,962,964],{},[634,963,914],{"stretchy":603,"minsize":913},[916,965,966],{"width":918,"lspace":919},[589,967,968,970],{},[634,969,924],{},[592,971,639],{},[592,973,974],{},"15",[909,976,977,979],{},[634,978,914],{"stretchy":603,"minsize":913},[916,980,981],{"width":918,"lspace":919},[589,982,983,985],{},[634,984,924],{},[592,986,639],{},[592,988,644],{},[596,990,991],{"encoding":598},"360 \\xrightarrow{:2} 180 \\xrightarrow{:2} 90 \\xrightarrow{:2} 45 \\xrightarrow{:3} 15 \\xrightarrow{:3} 5",[573,993,995,1095,1163,1231,1299,1367],{"className":994,"ariaHidden":603},[602],[573,996,998,1002,1005,1009,1092],{"className":997},[607],[573,999],{"className":1000,"style":1001},[611],"height:1.0841em;vertical-align:-0.011em;",[573,1003,873],{"className":1004},[616],[573,1006],{"className":1007,"style":1008},[698],"margin-right:0.2778em;",[573,1010,1014],{"className":1011},[1012,1013],"mrel","x-arrow",[573,1015,1019,1083],{"className":1016},[1017,1018],"vlist-t","vlist-t2",[573,1020,1023,1078],{"className":1021},[1022],"vlist-r",[573,1024,1028,1053],{"className":1025,"style":1027},[1026],"vlist","height:1.0731em;",[573,1029,1031,1036],{"style":1030},"top:-3.322em;",[573,1032],{"className":1033,"style":1035},[1034],"pstrut","height:2.7em;",[573,1037,1044],{"className":1038},[1039,1040,1041,1042,1043],"sizing","reset-size6","size3","mtight","x-arrow-pad",[573,1045,1047,1050],{"className":1046},[616,1042],[573,1048,924],{"className":1049},[1012,1042],[573,1051,632],{"className":1052},[616,1042],[573,1054,1058,1061],{"className":1055,"style":1057},[1056],"svg-align","top:-2.689em;",[573,1059],{"className":1060,"style":1035},[1034],[573,1062,1066],{"className":1063,"style":1065},[1064],"hide-tail","height:0.522em;min-width:1.469em;",[1067,1068,1074],"svg",{"xmlns":1069,"width":1070,"height":1071,"viewBox":1072,"preserveAspectRatio":1073},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","0.522em","0 0 400000 522","xMaxYMin slice",[1075,1076],"path",{"d":1077},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[573,1079,1082],{"className":1080},[1081],"vlist-s","​",[573,1084,1086],{"className":1085},[1022],[573,1087,1090],{"className":1088,"style":1089},[1026],"height:0.011em;",[573,1091],{},[573,1093],{"className":1094,"style":1008},[698],[573,1096,1098,1101,1104,1107,1160],{"className":1097},[607],[573,1099],{"className":1100,"style":1001},[611],[573,1102,929],{"className":1103},[616],[573,1105],{"className":1106,"style":1008},[698],[573,1108,1110],{"className":1109},[1012,1013],[573,1111,1113,1152],{"className":1112},[1017,1018],[573,1114,1116,1149],{"className":1115},[1022],[573,1117,1119,1136],{"className":1118,"style":1027},[1026],[573,1120,1121,1124],{"style":1030},[573,1122],{"className":1123,"style":1035},[1034],[573,1125,1127],{"className":1126},[1039,1040,1041,1042,1043],[573,1128,1130,1133],{"className":1129},[616,1042],[573,1131,924],{"className":1132},[1012,1042],[573,1134,632],{"className":1135},[616,1042],[573,1137,1139,1142],{"className":1138,"style":1057},[1056],[573,1140],{"className":1141,"style":1035},[1034],[573,1143,1145],{"className":1144,"style":1065},[1064],[1067,1146,1147],{"xmlns":1069,"width":1070,"height":1071,"viewBox":1072,"preserveAspectRatio":1073},[1075,1148],{"d":1077},[573,1150,1082],{"className":1151},[1081],[573,1153,1155],{"className":1154},[1022],[573,1156,1158],{"className":1157,"style":1089},[1026],[573,1159],{},[573,1161],{"className":1162,"style":1008},[698],[573,1164,1166,1169,1172,1175,1228],{"className":1165},[607],[573,1167],{"className":1168,"style":1001},[611],[573,1170,944],{"className":1171},[616],[573,1173],{"className":1174,"style":1008},[698],[573,1176,1178],{"className":1177},[1012,1013],[573,1179,1181,1220],{"className":1180},[1017,1018],[573,1182,1184,1217],{"className":1183},[1022],[573,1185,1187,1204],{"className":1186,"style":1027},[1026],[573,1188,1189,1192],{"style":1030},[573,1190],{"className":1191,"style":1035},[1034],[573,1193,1195],{"className":1194},[1039,1040,1041,1042,1043],[573,1196,1198,1201],{"className":1197},[616,1042],[573,1199,924],{"className":1200},[1012,1042],[573,1202,632],{"className":1203},[616,1042],[573,1205,1207,1210],{"className":1206,"style":1057},[1056],[573,1208],{"className":1209,"style":1035},[1034],[573,1211,1213],{"className":1212,"style":1065},[1064],[1067,1214,1215],{"xmlns":1069,"width":1070,"height":1071,"viewBox":1072,"preserveAspectRatio":1073},[1075,1216],{"d":1077},[573,1218,1082],{"className":1219},[1081],[573,1221,1223],{"className":1222},[1022],[573,1224,1226],{"className":1225,"style":1089},[1026],[573,1227],{},[573,1229],{"className":1230,"style":1008},[698],[573,1232,1234,1237,1240,1243,1296],{"className":1233},[607],[573,1235],{"className":1236,"style":1001},[611],[573,1238,959],{"className":1239},[616],[573,1241],{"className":1242,"style":1008},[698],[573,1244,1246],{"className":1245},[1012,1013],[573,1247,1249,1288],{"className":1248},[1017,1018],[573,1250,1252,1285],{"className":1251},[1022],[573,1253,1255,1272],{"className":1254,"style":1027},[1026],[573,1256,1257,1260],{"style":1030},[573,1258],{"className":1259,"style":1035},[1034],[573,1261,1263],{"className":1262},[1039,1040,1041,1042,1043],[573,1264,1266,1269],{"className":1265},[616,1042],[573,1267,924],{"className":1268},[1012,1042],[573,1270,639],{"className":1271},[616,1042],[573,1273,1275,1278],{"className":1274,"style":1057},[1056],[573,1276],{"className":1277,"style":1035},[1034],[573,1279,1281],{"className":1280,"style":1065},[1064],[1067,1282,1283],{"xmlns":1069,"width":1070,"height":1071,"viewBox":1072,"preserveAspectRatio":1073},[1075,1284],{"d":1077},[573,1286,1082],{"className":1287},[1081],[573,1289,1291],{"className":1290},[1022],[573,1292,1294],{"className":1293,"style":1089},[1026],[573,1295],{},[573,1297],{"className":1298,"style":1008},[698],[573,1300,1302,1305,1308,1311,1364],{"className":1301},[607],[573,1303],{"className":1304,"style":1001},[611],[573,1306,974],{"className":1307},[616],[573,1309],{"className":1310,"style":1008},[698],[573,1312,1314],{"className":1313},[1012,1013],[573,1315,1317,1356],{"className":1316},[1017,1018],[573,1318,1320,1353],{"className":1319},[1022],[573,1321,1323,1340],{"className":1322,"style":1027},[1026],[573,1324,1325,1328],{"style":1030},[573,1326],{"className":1327,"style":1035},[1034],[573,1329,1331],{"className":1330},[1039,1040,1041,1042,1043],[573,1332,1334,1337],{"className":1333},[616,1042],[573,1335,924],{"className":1336},[1012,1042],[573,1338,639],{"className":1339},[616,1042],[573,1341,1343,1346],{"className":1342,"style":1057},[1056],[573,1344],{"className":1345,"style":1035},[1034],[573,1347,1349],{"className":1348,"style":1065},[1064],[1067,1350,1351],{"xmlns":1069,"width":1070,"height":1071,"viewBox":1072,"preserveAspectRatio":1073},[1075,1352],{"d":1077},[573,1354,1082],{"className":1355},[1081],[573,1357,1359],{"className":1358},[1022],[573,1360,1362],{"className":1361,"style":1089},[1026],[573,1363],{},[573,1365],{"className":1366,"style":1008},[698],[573,1368,1370,1373],{"className":1369},[607],[573,1371],{"className":1372,"style":612},[611],[573,1374,644],{"className":1375},[616],[564,1377,1378,1379,1407],{},"Die ",[573,1380,1382,1395],{"className":1381},[576],[573,1383,1385],{"className":1384},[580],[582,1386,1387],{"xmlns":584},[586,1388,1389,1393],{},[589,1390,1391],{},[592,1392,644],{},[596,1394,644],{"encoding":598},[573,1396,1398],{"className":1397,"ariaHidden":603},[602],[573,1399,1401,1404],{"className":1400},[607],[573,1402],{"className":1403,"style":612},[611],[573,1405,644],{"className":1406},[616]," ist eine Primzahl, also ist man fertig:",[573,1409,1411],{"className":1410},[892],[573,1412,1414,1475],{"className":1413},[576],[573,1415,1417],{"className":1416},[580],[582,1418,1419],{"xmlns":584,"display":901},[586,1420,1421,1472],{},[589,1422,1423,1425,1428,1430,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1460,1462,1468,1470],{},[592,1424,873],{},[634,1426,1427],{},"=",[592,1429,632],{},[634,1431,1432],{},"⋅",[592,1434,632],{},[634,1436,1432],{},[592,1438,632],{},[634,1440,1432],{},[592,1442,639],{},[634,1444,1432],{},[592,1446,639],{},[634,1448,1432],{},[592,1450,644],{},[634,1452,1427],{},[1454,1455,1456,1458],"msup",{},[592,1457,632],{},[592,1459,639],{},[634,1461,1432],{},[1454,1463,1464,1466],{},[592,1465,639],{},[592,1467,632],{},[634,1469,1432],{},[592,1471,644],{},[596,1473,1474],{"encoding":598},"360 = 2 \\cdot 2 \\cdot 2 \\cdot 3 \\cdot 3 \\cdot 5 = 2^3 \\cdot 3^2 \\cdot 5",[573,1476,1478,1496,1516,1534,1552,1570,1588,1606,1653,1697],{"className":1477,"ariaHidden":603},[602],[573,1479,1481,1484,1487,1490,1493],{"className":1480},[607],[573,1482],{"className":1483,"style":612},[611],[573,1485,873],{"className":1486},[616],[573,1488],{"className":1489,"style":1008},[698],[573,1491,1427],{"className":1492},[1012],[573,1494],{"className":1495,"style":1008},[698],[573,1497,1499,1502,1505,1509,1513],{"className":1498},[607],[573,1500],{"className":1501,"style":612},[611],[573,1503,632],{"className":1504},[616],[573,1506],{"className":1507,"style":1508},[698],"margin-right:0.2222em;",[573,1510,1432],{"className":1511},[1512],"mbin",[573,1514],{"className":1515,"style":1508},[698],[573,1517,1519,1522,1525,1528,1531],{"className":1518},[607],[573,1520],{"className":1521,"style":612},[611],[573,1523,632],{"className":1524},[616],[573,1526],{"className":1527,"style":1508},[698],[573,1529,1432],{"className":1530},[1512],[573,1532],{"className":1533,"style":1508},[698],[573,1535,1537,1540,1543,1546,1549],{"className":1536},[607],[573,1538],{"className":1539,"style":612},[611],[573,1541,632],{"className":1542},[616],[573,1544],{"className":1545,"style":1508},[698],[573,1547,1432],{"className":1548},[1512],[573,1550],{"className":1551,"style":1508},[698],[573,1553,1555,1558,1561,1564,1567],{"className":1554},[607],[573,1556],{"className":1557,"style":612},[611],[573,1559,639],{"className":1560},[616],[573,1562],{"className":1563,"style":1508},[698],[573,1565,1432],{"className":1566},[1512],[573,1568],{"className":1569,"style":1508},[698],[573,1571,1573,1576,1579,1582,1585],{"className":1572},[607],[573,1574],{"className":1575,"style":612},[611],[573,1577,639],{"className":1578},[616],[573,1580],{"className":1581,"style":1508},[698],[573,1583,1432],{"className":1584},[1512],[573,1586],{"className":1587,"style":1508},[698],[573,1589,1591,1594,1597,1600,1603],{"className":1590},[607],[573,1592],{"className":1593,"style":612},[611],[573,1595,644],{"className":1596},[616],[573,1598],{"className":1599,"style":1008},[698],[573,1601,1427],{"className":1602},[1012],[573,1604],{"className":1605,"style":1008},[698],[573,1607,1609,1613,1644,1647,1650],{"className":1608},[607],[573,1610],{"className":1611,"style":1612},[611],"height:0.8641em;",[573,1614,1616,1619],{"className":1615},[616],[573,1617,632],{"className":1618},[616],[573,1620,1623],{"className":1621},[1622],"msupsub",[573,1624,1626],{"className":1625},[1017],[573,1627,1629],{"className":1628},[1022],[573,1630,1632],{"className":1631,"style":1612},[1026],[573,1633,1635,1638],{"style":1634},"top:-3.113em;margin-right:0.05em;",[573,1636],{"className":1637,"style":1035},[1034],[573,1639,1641],{"className":1640},[1039,1040,1041,1042],[573,1642,639],{"className":1643},[616,1042],[573,1645],{"className":1646,"style":1508},[698],[573,1648,1432],{"className":1649},[1512],[573,1651],{"className":1652,"style":1508},[698],[573,1654,1656,1659,1688,1691,1694],{"className":1655},[607],[573,1657],{"className":1658,"style":1612},[611],[573,1660,1662,1665],{"className":1661},[616],[573,1663,639],{"className":1664},[616],[573,1666,1668],{"className":1667},[1622],[573,1669,1671],{"className":1670},[1017],[573,1672,1674],{"className":1673},[1022],[573,1675,1677],{"className":1676,"style":1612},[1026],[573,1678,1679,1682],{"style":1634},[573,1680],{"className":1681,"style":1035},[1034],[573,1683,1685],{"className":1684},[1039,1040,1041,1042],[573,1686,632],{"className":1687},[616,1042],[573,1689],{"className":1690,"style":1508},[698],[573,1692,1432],{"className":1693},[1512],[573,1695],{"className":1696,"style":1508},[698],[573,1698,1700,1703],{"className":1699},[607],[573,1701],{"className":1702,"style":612},[611],[573,1704,644],{"className":1705},[616],[564,1707,1708,1709,1837],{},"Genauso ergibt sich ",[573,1710,1712,1743],{"className":1711},[576],[573,1713,1715],{"className":1714},[580],[582,1716,1717],{"xmlns":584},[586,1718,1719,1740],{},[589,1720,1721,1724,1726,1732,1734,1736,1738],{},[592,1722,1723],{},"84",[634,1725,1427],{},[1454,1727,1728,1730],{},[592,1729,632],{},[592,1731,632],{},[634,1733,1432],{},[592,1735,639],{},[634,1737,1432],{},[592,1739,649],{},[596,1741,1742],{"encoding":598},"84 = 2^2 \\cdot 3 \\cdot 7",[573,1744,1746,1764,1810,1828],{"className":1745,"ariaHidden":603},[602],[573,1747,1749,1752,1755,1758,1761],{"className":1748},[607],[573,1750],{"className":1751,"style":612},[611],[573,1753,1723],{"className":1754},[616],[573,1756],{"className":1757,"style":1008},[698],[573,1759,1427],{"className":1760},[1012],[573,1762],{"className":1763,"style":1008},[698],[573,1765,1767,1771,1801,1804,1807],{"className":1766},[607],[573,1768],{"className":1769,"style":1770},[611],"height:0.8141em;",[573,1772,1774,1777],{"className":1773},[616],[573,1775,632],{"className":1776},[616],[573,1778,1780],{"className":1779},[1622],[573,1781,1783],{"className":1782},[1017],[573,1784,1786],{"className":1785},[1022],[573,1787,1789],{"className":1788,"style":1770},[1026],[573,1790,1792,1795],{"style":1791},"top:-3.063em;margin-right:0.05em;",[573,1793],{"className":1794,"style":1035},[1034],[573,1796,1798],{"className":1797},[1039,1040,1041,1042],[573,1799,632],{"className":1800},[616,1042],[573,1802],{"className":1803,"style":1508},[698],[573,1805,1432],{"className":1806},[1512],[573,1808],{"className":1809,"style":1508},[698],[573,1811,1813,1816,1819,1822,1825],{"className":1812},[607],[573,1814],{"className":1815,"style":612},[611],[573,1817,639],{"className":1818},[616],[573,1820],{"className":1821,"style":1508},[698],[573,1823,1432],{"className":1824},[1512],[573,1826],{"className":1827,"style":1508},[698],[573,1829,1831,1834],{"className":1830},[607],[573,1832],{"className":1833,"style":612},[611],[573,1835,649],{"className":1836},[616],".",[564,1839,1840,1841,1870,1871,1899,1900,1968,1969,2056,2057,2085,2086,2114],{},"Ist ",[573,1842,1844,1858],{"className":1843},[576],[573,1845,1847],{"className":1846},[580],[582,1848,1849],{"xmlns":584},[586,1850,1851,1856],{},[589,1852,1853],{},[592,1854,1855],{},"97",[596,1857,1855],{"encoding":598},[573,1859,1861],{"className":1860,"ariaHidden":603},[602],[573,1862,1864,1867],{"className":1863},[607],[573,1865],{"className":1866,"style":612},[611],[573,1868,1855],{"className":1869},[616]," eine Primzahl? Man muss nur die Primzahlen testen, deren Quadrat höchstens ",[573,1872,1874,1887],{"className":1873},[576],[573,1875,1877],{"className":1876},[580],[582,1878,1879],{"xmlns":584},[586,1880,1881,1885],{},[589,1882,1883],{},[592,1884,1855],{},[596,1886,1855],{"encoding":598},[573,1888,1890],{"className":1889,"ariaHidden":603},[602],[573,1891,1893,1896],{"className":1892},[607],[573,1894],{"className":1895,"style":612},[611],[573,1897,1855],{"className":1898},[616]," ist, also ",[573,1901,1903,1929],{"className":1902},[576],[573,1904,1906],{"className":1905},[580],[582,1907,1908],{"xmlns":584},[586,1909,1910,1926],{},[589,1911,1912,1914,1916,1918,1920,1922,1924],{},[592,1913,632],{},[634,1915,636],{"separator":603},[592,1917,639],{},[634,1919,636],{"separator":603},[592,1921,644],{},[634,1923,636],{"separator":603},[592,1925,649],{},[596,1927,1928],{"encoding":598},"2, 3, 5, 7",[573,1930,1932],{"className":1931,"ariaHidden":603},[602],[573,1933,1935,1938,1941,1944,1947,1950,1953,1956,1959,1962,1965],{"className":1934},[607],[573,1936],{"className":1937,"style":687},[611],[573,1939,632],{"className":1940},[616],[573,1942,636],{"className":1943},[694],[573,1945],{"className":1946,"style":699},[698],[573,1948,639],{"className":1949},[616],[573,1951,636],{"className":1952},[694],[573,1954],{"className":1955,"style":699},[698],[573,1957,644],{"className":1958},[616],[573,1960,636],{"className":1961},[694],[573,1963],{"className":1964,"style":699},[698],[573,1966,649],{"className":1967},[616]," (denn ",[573,1970,1972,1996],{"className":1971},[576],[573,1973,1975],{"className":1974},[580],[582,1976,1977],{"xmlns":584},[586,1978,1979,1993],{},[589,1980,1981,1988,1990],{},[1454,1982,1983,1986],{},[592,1984,1985],{},"10",[592,1987,632],{},[634,1989,1427],{},[592,1991,1992],{},"100",[596,1994,1995],{"encoding":598},"10^2 = 100",[573,1997,1999,2047],{"className":1998,"ariaHidden":603},[602],[573,2000,2002,2005,2008,2038,2041,2044],{"className":2001},[607],[573,2003],{"className":2004,"style":1770},[611],[573,2006,594],{"className":2007},[616],[573,2009,2011,2015],{"className":2010},[616],[573,2012,2014],{"className":2013},[616],"0",[573,2016,2018],{"className":2017},[1622],[573,2019,2021],{"className":2020},[1017],[573,2022,2024],{"className":2023},[1022],[573,2025,2027],{"className":2026,"style":1770},[1026],[573,2028,2029,2032],{"style":1791},[573,2030],{"className":2031,"style":1035},[1034],[573,2033,2035],{"className":2034},[1039,1040,1041,1042],[573,2036,632],{"className":2037},[616,1042],[573,2039],{"className":2040,"style":1008},[698],[573,2042,1427],{"className":2043},[1012],[573,2045],{"className":2046,"style":1008},[698],[573,2048,2050,2053],{"className":2049},[607],[573,2051],{"className":2052,"style":612},[611],[573,2054,1992],{"className":2055},[616]," ist schon zu groß). Keine davon teilt ",[573,2058,2060,2073],{"className":2059},[576],[573,2061,2063],{"className":2062},[580],[582,2064,2065],{"xmlns":584},[586,2066,2067,2071],{},[589,2068,2069],{},[592,2070,1855],{},[596,2072,1855],{"encoding":598},[573,2074,2076],{"className":2075,"ariaHidden":603},[602],[573,2077,2079,2082],{"className":2078},[607],[573,2080],{"className":2081,"style":612},[611],[573,2083,1855],{"className":2084},[616]," ohne Rest. Also ist ",[573,2087,2089,2102],{"className":2088},[576],[573,2090,2092],{"className":2091},[580],[582,2093,2094],{"xmlns":584},[586,2095,2096,2100],{},[589,2097,2098],{},[592,2099,1855],{},[596,2101,1855],{"encoding":598},[573,2103,2105],{"className":2104,"ariaHidden":603},[602],[573,2106,2108,2111],{"className":2107},[607],[573,2109],{"className":2110,"style":612},[611],[573,2112,1855],{"className":2113},[616]," eine Primzahl.",[559,2116,2118],{"id":2117},"typische-fehler","Typische Fehler",[2120,2121,2122,2310,2341],"ul",{},[840,2123,2124,2125,2222,2223,2251,2252,2280,2281,2309],{},"Mit Zahlen aufhören, die keine Primzahlen sind: ",[573,2126,2128,2156],{"className":2127},[576],[573,2129,2131],{"className":2130},[580],[582,2132,2133],{"xmlns":584},[586,2134,2135,2153],{},[589,2136,2137,2139,2141,2144,2146,2149,2151],{},[592,2138,873],{},[634,2140,1427],{},[592,2142,2143],{},"4",[634,2145,1432],{},[592,2147,2148],{},"9",[634,2150,1432],{},[592,2152,1985],{},[596,2154,2155],{"encoding":598},"360 = 4 \\cdot 9 \\cdot 10",[573,2157,2159,2177,2195,2213],{"className":2158,"ariaHidden":603},[602],[573,2160,2162,2165,2168,2171,2174],{"className":2161},[607],[573,2163],{"className":2164,"style":612},[611],[573,2166,873],{"className":2167},[616],[573,2169],{"className":2170,"style":1008},[698],[573,2172,1427],{"className":2173},[1012],[573,2175],{"className":2176,"style":1008},[698],[573,2178,2180,2183,2186,2189,2192],{"className":2179},[607],[573,2181],{"className":2182,"style":612},[611],[573,2184,2143],{"className":2185},[616],[573,2187],{"className":2188,"style":1508},[698],[573,2190,1432],{"className":2191},[1512],[573,2193],{"className":2194,"style":1508},[698],[573,2196,2198,2201,2204,2207,2210],{"className":2197},[607],[573,2199],{"className":2200,"style":612},[611],[573,2202,2148],{"className":2203},[616],[573,2205],{"className":2206,"style":1508},[698],[573,2208,1432],{"className":2209},[1512],[573,2211],{"className":2212,"style":1508},[698],[573,2214,2216,2219],{"className":2215},[607],[573,2217],{"className":2218,"style":612},[611],[573,2220,1985],{"className":2221},[616]," stimmt zwar, ist aber keine Primfaktorzerlegung. ",[573,2224,2226,2239],{"className":2225},[576],[573,2227,2229],{"className":2228},[580],[582,2230,2231],{"xmlns":584},[586,2232,2233,2237],{},[589,2234,2235],{},[592,2236,2143],{},[596,2238,2143],{"encoding":598},[573,2240,2242],{"className":2241,"ariaHidden":603},[602],[573,2243,2245,2248],{"className":2244},[607],[573,2246],{"className":2247,"style":612},[611],[573,2249,2143],{"className":2250},[616],", ",[573,2253,2255,2268],{"className":2254},[576],[573,2256,2258],{"className":2257},[580],[582,2259,2260],{"xmlns":584},[586,2261,2262,2266],{},[589,2263,2264],{},[592,2265,2148],{},[596,2267,2148],{"encoding":598},[573,2269,2271],{"className":2270,"ariaHidden":603},[602],[573,2272,2274,2277],{"className":2273},[607],[573,2275],{"className":2276,"style":612},[611],[573,2278,2148],{"className":2279},[616]," und ",[573,2282,2284,2297],{"className":2283},[576],[573,2285,2287],{"className":2286},[580],[582,2288,2289],{"xmlns":584},[586,2290,2291,2295],{},[589,2292,2293],{},[592,2294,1985],{},[596,2296,1985],{"encoding":598},[573,2298,2300],{"className":2299,"ariaHidden":603},[602],[573,2301,2303,2306],{"className":2302},[607],[573,2304],{"className":2305,"style":612},[611],[573,2307,1985],{"className":2308},[616]," müssen weiter zerlegt werden.",[840,2311,1378,2312,2340],{},[573,2313,2315,2328],{"className":2314},[576],[573,2316,2318],{"className":2317},[580],[582,2319,2320],{"xmlns":584},[586,2321,2322,2326],{},[589,2323,2324],{},[592,2325,594],{},[596,2327,594],{"encoding":598},[573,2329,2331],{"className":2330,"ariaHidden":603},[602],[573,2332,2334,2337],{"className":2333},[607],[573,2335],{"className":2336,"style":612},[611],[573,2338,594],{"className":2339},[616]," als Primfaktor aufschreiben. Sie gehört nicht in die Zerlegung.",[840,2342,2343,2344,2372,2373,2432,2433,1837],{},"Einen Faktor beim Zusammenfassen vergessen: Kommt die ",[573,2345,2347,2360],{"className":2346},[576],[573,2348,2350],{"className":2349},[580],[582,2351,2352],{"xmlns":584},[586,2353,2354,2358],{},[589,2355,2356],{},[592,2357,632],{},[596,2359,632],{"encoding":598},[573,2361,2363],{"className":2362,"ariaHidden":603},[602],[573,2364,2366,2369],{"className":2365},[607],[573,2367],{"className":2368,"style":612},[611],[573,2370,632],{"className":2371},[616]," dreimal vor, heißt es ",[573,2374,2376,2394],{"className":2375},[576],[573,2377,2379],{"className":2378},[580],[582,2380,2381],{"xmlns":584},[586,2382,2383,2391],{},[589,2384,2385],{},[1454,2386,2387,2389],{},[592,2388,632],{},[592,2390,639],{},[596,2392,2393],{"encoding":598},"2^3",[573,2395,2397],{"className":2396,"ariaHidden":603},[602],[573,2398,2400,2403],{"className":2399},[607],[573,2401],{"className":2402,"style":1770},[611],[573,2404,2406,2409],{"className":2405},[616],[573,2407,632],{"className":2408},[616],[573,2410,2412],{"className":2411},[1622],[573,2413,2415],{"className":2414},[1017],[573,2416,2418],{"className":2417},[1022],[573,2419,2421],{"className":2420,"style":1770},[1026],[573,2422,2423,2426],{"style":1791},[573,2424],{"className":2425,"style":1035},[1034],[573,2427,2429],{"className":2428},[1039,1040,1041,1042],[573,2430,639],{"className":2431},[616,1042],", nicht ",[573,2434,2436,2454],{"className":2435},[576],[573,2437,2439],{"className":2438},[580],[582,2440,2441],{"xmlns":584},[586,2442,2443,2451],{},[589,2444,2445],{},[1454,2446,2447,2449],{},[592,2448,632],{},[592,2450,632],{},[596,2452,2453],{"encoding":598},"2^2",[573,2455,2457],{"className":2456,"ariaHidden":603},[602],[573,2458,2460,2463],{"className":2459},[607],[573,2461],{"className":2462,"style":1770},[611],[573,2464,2466,2469],{"className":2465},[616],[573,2467,632],{"className":2468},[616],[573,2470,2472],{"className":2471},[1622],[573,2473,2475],{"className":2474},[1017],[573,2476,2478],{"className":2477},[1022],[573,2479,2481],{"className":2480,"style":1770},[1026],[573,2482,2483,2486],{"style":1791},[573,2484],{"className":2485,"style":1035},[1034],[573,2487,2489],{"className":2488},[1039,1040,1041,1042],[573,2490,632],{"className":2491},[616,1042],{"title":2493,"searchDepth":2494,"depth":2494,"links":2495},"",2,[2496,2497,2498],{"id":561,"depth":2494,"text":562},{"id":854,"depth":2494,"text":855},{"id":2117,"depth":2494,"text":2118},[2500,2502,2504,2506,2508,2510,2512,2514,2516,2518,2520,2523,2525],{"lhs":2501,"rhs":873},"2^3 * 3^2 * 5",{"lhs":2503,"rhs":929},"360\u002F2",{"lhs":2505,"rhs":944},"180\u002F2",{"lhs":2507,"rhs":959},"90\u002F2",{"lhs":2509,"rhs":974},"45\u002F3",{"lhs":2511,"rhs":644},"15\u002F3",{"lhs":2513,"rhs":1723},"2^2 * 3 * 7",{"lhs":2515,"rhs":594},"mod(97, 2)",{"lhs":2517,"rhs":594},"mod(97, 3)",{"lhs":2519,"rhs":632},"mod(97, 5)",{"lhs":2521,"rhs":2522},"mod(97, 7)","6",{"lhs":2524,"rhs":1992},"10^2",{"lhs":2526,"rhs":873},"4 * 9 * 10","n \\in \\mathbb{N},\\ n \\geq 2","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","prime-factorization","n = p_1^{k_1} \\cdot p_2^{k_2} \\cdot \\ldots \\cdot p_r^{k_r}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmsubsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n = p_1^{k_1} \\cdot p_2^{k_2} \\cdot \\ldots \\cdot p_r^{k_r}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1973em;vertical-align:-0.2663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.931em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.1449em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2663em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1973em;vertical-align:-0.2663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.931em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.1449em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2663em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1461em;vertical-align:-0.247em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\u003Cspan style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1645em;\">\u003Cspan style=\"top:-2.357em;margin-left:-0.0315em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung",[],[2540,2541,2542],"divisibility-rules","gcd-lcm","fraction-reducing",{"title":548,"description":2493},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung","Jede natürliche Zahl ab 2 lässt sich auf genau eine Weise als Produkt von Primzahlen schreiben.",[2547,2548,2549,2550],"primzahl","primfaktor","teiler","zerlegung",[2552,2556,2560],{"symbol":2553,"meaning":2554,"symbolHtml":2555},"n","die zu zerlegende natürliche Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2557,"meaning":2558,"symbolHtml":2559},"p_1, \\ldots, p_r","verschiedene Primzahlen, der Größe nach geordnet","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1, \\ldots, p_r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2561,"meaning":2562,"symbolHtml":2563},"k_1, \\ldots, k_r","Exponenten, wie oft jeder Primfaktor vorkommt (mindestens 1)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k_1, \\ldots, k_r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","IifGrwrh-Ic94iZ75vvdONLz4k7MWe0D1oge6xXPDdU",[2566,2569,2572],{"stem":2567,"title":2568,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-kuerzen-und-erweitern","Brüche kürzen und erweitern",{"stem":2570,"title":2571,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv","Zusammenhang von ggT und kgV",{"stem":2573,"title":2574,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fteilbarkeitsregeln","Teilbarkeitsregeln",1793824259795]