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",[585,997,999,1012],{"className":998},[588],[585,1000,1002],{"className":1001},[592],[594,1003,1004],{"xmlns":596},[598,1005,1006,1010],{},[601,1007,1008],{},[604,1009,950],{},[608,1011,950],{"encoding":610},[585,1013,1015],{"className":1014,"ariaHidden":615},[614],[585,1016,1018,1021],{"className":1017},[619],[585,1019],{"className":1020,"style":624},[623],[585,1022,950],{"className":1023},[628],[585,1025,1027,1041],{"className":1026},[588],[585,1028,1030],{"className":1029},[592],[594,1031,1032],{"xmlns":596},[598,1033,1034,1039],{},[601,1035,1036],{},[604,1037,1038],{},"50",[608,1040,1038],{"encoding":610},[585,1042,1044],{"className":1043,"ariaHidden":615},[614],[585,1045,1047,1050],{"className":1046},[619],[585,1048],{"className":1049,"style":624},[623],[585,1051,1038],{"className":1052},[628],[585,1054,1056,1070],{"className":1055},[588],[585,1057,1059],{"className":1058},[592],[594,1060,1061],{"xmlns":596},[598,1062,1063,1068],{},[601,1064,1065],{},[604,1066,1067],{},"75",[608,1069,1067],{"encoding":610},[585,1071,1073],{"className":1072,"ariaHidden":615},[614],[585,1074,1076,1079],{"className":1075},[619],[585,1077],{"className":1078,"style":624},[623],[585,1080,1067],{"className":1081},[628],[581,1083,583,1084,900,1112,904,1115,1143],{},[585,1085,1087,1100],{"className":1086},[588],[585,1088,1090],{"className":1089},[592],[594,1091,1092],{"xmlns":596},[598,1093,1094,1098],{},[601,1095,1096],{},[604,1097,665],{},[608,1099,665],{"encoding":610},[585,1101,1103],{"className":1102,"ariaHidden":615},[614],[585,1104,1106,1109],{"className":1105},[619],[585,1107],{"className":1108,"style":624},[623],[585,1110,665],{"className":1111},[628],[568,1113,1114],{},"drei",[585,1116,1118,1131],{"className":1117},[588],[585,1119,1121],{"className":1120},[592],[594,1122,1123],{"xmlns":596},[598,1124,1125,1129],{},[601,1126,1127],{},[604,1128,665],{},[608,1130,665],{"encoding":610},[585,1132,1134],{"className":1133,"ariaHidden":615},[614],[585,1135,1137,1140],{"className":1136},[619],[585,1138],{"className":1139,"style":624},[623],[585,1141,665],{"className":1142},[628]," teilbar.",[564,1145,1146,1149,1150,1153],{},[568,1147,1148],{},"Regeln mit der Quersumme:"," Die ",[568,1151,1152],{},"Quersumme"," ist die Summe aller Ziffern einer Zahl.",[578,1155,1156,1216],{},[581,1157,583,1158,1187,1188,933],{},[585,1159,1161,1175],{"className":1160},[588],[585,1162,1164],{"className":1163},[592],[594,1165,1166],{"xmlns":596},[598,1167,1168,1173],{},[601,1169,1170],{},[604,1171,1172],{},"3",[608,1174,1172],{"encoding":610},[585,1176,1178],{"className":1177,"ariaHidden":615},[614],[585,1179,1181,1184],{"className":1180},[619],[585,1182],{"className":1183,"style":624},[623],[585,1185,1172],{"className":1186},[628],": die Quersumme ist durch ",[585,1189,1191,1204],{"className":1190},[588],[585,1192,1194],{"className":1193},[592],[594,1195,1196],{"xmlns":596},[598,1197,1198,1202],{},[601,1199,1200],{},[604,1201,1172],{},[608,1203,1172],{"encoding":610},[585,1205,1207],{"className":1206,"ariaHidden":615},[614],[585,1208,1210,1213],{"className":1209},[619],[585,1211],{"className":1212,"style":624},[623],[585,1214,1172],{"className":1215},[628],[581,1217,583,1218,1187,1247,1143],{},[585,1219,1221,1235],{"className":1220},[588],[585,1222,1224],{"className":1223},[592],[594,1225,1226],{"xmlns":596},[598,1227,1228,1233],{},[601,1229,1230],{},[604,1231,1232],{},"9",[608,1234,1232],{"encoding":610},[585,1236,1238],{"className":1237,"ariaHidden":615},[614],[585,1239,1241,1244],{"className":1240},[619],[585,1242],{"className":1243,"style":624},[623],[585,1245,1232],{"className":1246},[628],[585,1248,1250,1263],{"className":1249},[588],[585,1251,1253],{"className":1252},[592],[594,1254,1255],{"xmlns":596},[598,1256,1257,1261],{},[601,1258,1259],{},[604,1260,1232],{},[608,1262,1232],{"encoding":610},[585,1264,1266],{"className":1265,"ariaHidden":615},[614],[585,1267,1269,1272],{"className":1268},[619],[585,1270],{"className":1271,"style":624},[623],[585,1273,1232],{"className":1274},[628],[564,1276,1277,1280,1281,1309,1310,1338,1339,1342,1343,1371],{},[568,1278,1279],{},"Zusammengesetzte Regel:"," Eine Zahl ist durch ",[585,1282,1284,1297],{"className":1283},[588],[585,1285,1287],{"className":1286},[592],[594,1288,1289],{"xmlns":596},[598,1290,1291,1295],{},[601,1292,1293],{},[604,1294,660],{},[608,1296,660],{"encoding":610},[585,1298,1300],{"className":1299,"ariaHidden":615},[614],[585,1301,1303,1306],{"className":1302},[619],[585,1304],{"className":1305,"style":624},[623],[585,1307,660],{"className":1308},[628]," teilbar, wenn sie durch ",[585,1311,1313,1326],{"className":1312},[588],[585,1314,1316],{"className":1315},[592],[594,1317,1318],{"xmlns":596},[598,1319,1320,1324],{},[601,1321,1322],{},[604,1323,606],{},[608,1325,606],{"encoding":610},[585,1327,1329],{"className":1328,"ariaHidden":615},[614],[585,1330,1332,1335],{"className":1331},[619],[585,1333],{"className":1334,"style":624},[623],[585,1336,606],{"className":1337},[628]," ",[568,1340,1341],{},"und"," durch ",[585,1344,1346,1359],{"className":1345},[588],[585,1347,1349],{"className":1348},[592],[594,1350,1351],{"xmlns":596},[598,1352,1353,1357],{},[601,1354,1355],{},[604,1356,1172],{},[608,1358,1172],{"encoding":610},[585,1360,1362],{"className":1361,"ariaHidden":615},[614],[585,1363,1365,1368],{"className":1364},[619],[585,1366],{"className":1367,"style":624},[623],[585,1369,1172],{"className":1370},[628]," teilbar ist.",[559,1373,1375],{"id":1374},"herleitung","Herleitung",[564,1377,1378,1379,995,1411,995,1441,1470,1471,1560],{},"Warum klappt die Quersumme? Eine dreistellige Zahl mit den Ziffern ",[585,1380,1382,1397],{"className":1381},[588],[585,1383,1385],{"className":1384},[592],[594,1386,1387],{"xmlns":596},[598,1388,1389,1395],{},[601,1390,1391],{},[1392,1393,1394],"mi",{},"a",[608,1396,1394],{"encoding":610},[585,1398,1400],{"className":1399,"ariaHidden":615},[614],[585,1401,1403,1407],{"className":1402},[619],[585,1404],{"className":1405,"style":1406},[623],"height:0.4306em;",[585,1408,1394],{"className":1409},[628,1410],"mathnormal",[585,1412,1414,1428],{"className":1413},[588],[585,1415,1417],{"className":1416},[592],[594,1418,1419],{"xmlns":596},[598,1420,1421,1426],{},[601,1422,1423],{},[1392,1424,1425],{},"b",[608,1427,1425],{"encoding":610},[585,1429,1431],{"className":1430,"ariaHidden":615},[614],[585,1432,1434,1438],{"className":1433},[619],[585,1435],{"className":1436,"style":1437},[623],"height:0.6944em;",[585,1439,1425],{"className":1440},[628,1410],[585,1442,1444,1458],{"className":1443},[588],[585,1445,1447],{"className":1446},[592],[594,1448,1449],{"xmlns":596},[598,1450,1451,1456],{},[601,1452,1453],{},[1392,1454,1455],{},"c",[608,1457,1455],{"encoding":610},[585,1459,1461],{"className":1460,"ariaHidden":615},[614],[585,1462,1464,1467],{"className":1463},[619],[585,1465],{"className":1466,"style":1406},[623],[585,1468,1455],{"className":1469},[628,1410]," hat den Wert ",[585,1472,1474,1502],{"className":1473},[588],[585,1475,1477],{"className":1476},[592],[594,1478,1479],{"xmlns":596},[598,1480,1481,1499],{},[601,1482,1483,1486,1488,1491,1493,1495,1497],{},[604,1484,1485],{},"100",[1392,1487,1394],{},[646,1489,1490],{},"+",[604,1492,827],{},[1392,1494,1425],{},[646,1496,1490],{},[1392,1498,1455],{},[608,1500,1501],{"encoding":610},"100a + 10b + c",[585,1503,1505,1529,1551],{"className":1504,"ariaHidden":615},[614],[585,1506,1508,1512,1515,1518,1522,1526],{"className":1507},[619],[585,1509],{"className":1510,"style":1511},[623],"height:0.7278em;vertical-align:-0.0833em;",[585,1513,1485],{"className":1514},[628],[585,1516,1394],{"className":1517},[628,1410],[585,1519],{"className":1520,"style":1521},[689],"margin-right:0.2222em;",[585,1523,1490],{"className":1524},[1525],"mbin",[585,1527],{"className":1528,"style":1521},[689],[585,1530,1532,1536,1539,1542,1545,1548],{"className":1531},[619],[585,1533],{"className":1534,"style":1535},[623],"height:0.7778em;vertical-align:-0.0833em;",[585,1537,827],{"className":1538},[628],[585,1540,1425],{"className":1541},[628,1410],[585,1543],{"className":1544,"style":1521},[689],[585,1546,1490],{"className":1547},[1525],[585,1549],{"className":1550,"style":1521},[689],[585,1552,1554,1557],{"className":1553},[619],[585,1555],{"className":1556,"style":1406},[623],[585,1558,1455],{"className":1559},[628,1410],". Zieht man die Quersumme ab, bleibt",[585,1562,1565],{"className":1563},[1564],"katex-display",[585,1566,1568,1649],{"className":1567},[588],[585,1569,1571],{"className":1570},[592],[594,1572,1574],{"xmlns":596,"display":1573},"block",[598,1575,1576,1646],{},[601,1577,1578,1580,1582,1584,1586,1588,1590,1592,1595,1599,1601,1603,1605,1607,1609,1612,1615,1618,1620,1622,1624,1626,1628,1630,1633,1635,1638,1640,1642,1644],{},[604,1579,1485],{},[1392,1581,1394],{},[646,1583,1490],{},[604,1585,827],{},[1392,1587,1425],{},[646,1589,1490],{},[1392,1591,1455],{},[646,1593,1594],{},"−",[646,1596,1598],{"stretchy":1597},"false","(",[1392,1600,1394],{},[646,1602,1490],{},[1392,1604,1425],{},[646,1606,1490],{},[1392,1608,1455],{},[646,1610,1611],{"stretchy":1597},")",[646,1613,1614],{},"=",[604,1616,1617],{},"99",[1392,1619,1394],{},[646,1621,1490],{},[604,1623,1232],{},[1392,1625,1425],{},[646,1627,1614],{},[604,1629,1232],{},[646,1631,1632],{},"⋅",[646,1634,1598],{"stretchy":1597},[604,1636,1637],{},"11",[1392,1639,1394],{},[646,1641,1490],{},[1392,1643,1425],{},[646,1645,1611],{"stretchy":1597},[608,1647,1648],{"encoding":610},"100a + 10b + c - (a + b + c) = 99a + 9b = 9 \\cdot (11a + b)",[585,1650,1652,1673,1694,1713,1736,1754,1778,1799,1820,1838,1862],{"className":1651,"ariaHidden":615},[614],[585,1653,1655,1658,1661,1664,1667,1670],{"className":1654},[619],[585,1656],{"className":1657,"style":1511},[623],[585,1659,1485],{"className":1660},[628],[585,1662,1394],{"className":1663},[628,1410],[585,1665],{"className":1666,"style":1521},[689],[585,1668,1490],{"className":1669},[1525],[585,1671],{"className":1672,"style":1521},[689],[585,1674,1676,1679,1682,1685,1688,1691],{"className":1675},[619],[585,1677],{"className":1678,"style":1535},[623],[585,1680,827],{"className":1681},[628],[585,1683,1425],{"className":1684},[628,1410],[585,1686],{"className":1687,"style":1521},[689],[585,1689,1490],{"className":1690},[1525],[585,1692],{"className":1693,"style":1521},[689],[585,1695,1697,1701,1704,1707,1710],{"className":1696},[619],[585,1698],{"className":1699,"style":1700},[623],"height:0.6667em;vertical-align:-0.0833em;",[585,1702,1455],{"className":1703},[628,1410],[585,1705],{"className":1706,"style":1521},[689],[585,1708,1594],{"className":1709},[1525],[585,1711],{"className":1712,"style":1521},[689],[585,1714,1716,1720,1724,1727,1730,1733],{"className":1715},[619],[585,1717],{"className":1718,"style":1719},[623],"height:1em;vertical-align:-0.25em;",[585,1721,1598],{"className":1722},[1723],"mopen",[585,1725,1394],{"className":1726},[628,1410],[585,1728],{"className":1729,"style":1521},[689],[585,1731,1490],{"className":1732},[1525],[585,1734],{"className":1735,"style":1521},[689],[585,1737,1739,1742,1745,1748,1751],{"className":1738},[619],[585,1740],{"className":1741,"style":1535},[623],[585,1743,1425],{"className":1744},[628,1410],[585,1746],{"className":1747,"style":1521},[689],[585,1749,1490],{"className":1750},[1525],[585,1752],{"className":1753,"style":1521},[689],[585,1755,1757,1760,1763,1767,1771,1775],{"className":1756},[619],[585,1758],{"className":1759,"style":1719},[623],[585,1761,1455],{"className":1762},[628,1410],[585,1764,1611],{"className":1765},[1766],"mclose",[585,1768],{"className":1769,"style":1770},[689],"margin-right:0.2778em;",[585,1772,1614],{"className":1773},[1774],"mrel",[585,1776],{"className":1777,"style":1770},[689],[585,1779,1781,1784,1787,1790,1793,1796],{"className":1780},[619],[585,1782],{"className":1783,"style":1511},[623],[585,1785,1617],{"className":1786},[628],[585,1788,1394],{"className":1789},[628,1410],[585,1791],{"className":1792,"style":1521},[689],[585,1794,1490],{"className":1795},[1525],[585,1797],{"className":1798,"style":1521},[689],[585,1800,1802,1805,1808,1811,1814,1817],{"className":1801},[619],[585,1803],{"className":1804,"style":1437},[623],[585,1806,1232],{"className":1807},[628],[585,1809,1425],{"className":1810},[628,1410],[585,1812],{"className":1813,"style":1770},[689],[585,1815,1614],{"className":1816},[1774],[585,1818],{"className":1819,"style":1770},[689],[585,1821,1823,1826,1829,1832,1835],{"className":1822},[619],[585,1824],{"className":1825,"style":624},[623],[585,1827,1232],{"className":1828},[628],[585,1830],{"className":1831,"style":1521},[689],[585,1833,1632],{"className":1834},[1525],[585,1836],{"className":1837,"style":1521},[689],[585,1839,1841,1844,1847,1850,1853,1856,1859],{"className":1840},[619],[585,1842],{"className":1843,"style":1719},[623],[585,1845,1598],{"className":1846},[1723],[585,1848,1637],{"className":1849},[628],[585,1851,1394],{"className":1852},[628,1410],[585,1854],{"className":1855,"style":1521},[689],[585,1857,1490],{"className":1858},[1525],[585,1860],{"className":1861,"style":1521},[689],[585,1863,1865,1868,1871],{"className":1864},[619],[585,1866],{"className":1867,"style":1719},[623],[585,1869,1425],{"className":1870},[628,1410],[585,1872,1611],{"className":1873},[1766],[564,1875,1876,1877,1905,1906,1934,1935,1963,1964,1992],{},"Dieser Unterschied ist immer durch ",[585,1878,1880,1893],{"className":1879},[588],[585,1881,1883],{"className":1882},[592],[594,1884,1885],{"xmlns":596},[598,1886,1887,1891],{},[601,1888,1889],{},[604,1890,1232],{},[608,1892,1232],{"encoding":610},[585,1894,1896],{"className":1895,"ariaHidden":615},[614],[585,1897,1899,1902],{"className":1898},[619],[585,1900],{"className":1901,"style":624},[623],[585,1903,1232],{"className":1904},[628]," und damit auch durch ",[585,1907,1909,1922],{"className":1908},[588],[585,1910,1912],{"className":1911},[592],[594,1913,1914],{"xmlns":596},[598,1915,1916,1920],{},[601,1917,1918],{},[604,1919,1172],{},[608,1921,1172],{"encoding":610},[585,1923,1925],{"className":1924,"ariaHidden":615},[614],[585,1926,1928,1931],{"className":1927},[619],[585,1929],{"className":1930,"style":624},[623],[585,1932,1172],{"className":1933},[628]," teilbar. Deshalb lässt die Zahl beim Teilen durch ",[585,1936,1938,1951],{"className":1937},[588],[585,1939,1941],{"className":1940},[592],[594,1942,1943],{"xmlns":596},[598,1944,1945,1949],{},[601,1946,1947],{},[604,1948,1232],{},[608,1950,1232],{"encoding":610},[585,1952,1954],{"className":1953,"ariaHidden":615},[614],[585,1955,1957,1960],{"className":1956},[619],[585,1958],{"className":1959,"style":624},[623],[585,1961,1232],{"className":1962},[628]," (oder ",[585,1965,1967,1980],{"className":1966},[588],[585,1968,1970],{"className":1969},[592],[594,1971,1972],{"xmlns":596},[598,1973,1974,1978],{},[601,1975,1976],{},[604,1977,1172],{},[608,1979,1172],{"encoding":610},[585,1981,1983],{"className":1982,"ariaHidden":615},[614],[585,1984,1986,1989],{"className":1985},[619],[585,1987],{"className":1988,"style":624},[623],[585,1990,1172],{"className":1991},[628],") denselben Rest wie ihre Quersumme. Für längere Zahlen funktioniert es genauso.",[559,1994,1996],{"id":1995},"beispiele","Beispiele",[564,1998,1999,2000,2029],{},"Die Zahl ",[585,2001,2003,2017],{"className":2002},[588],[585,2004,2006],{"className":2005},[592],[594,2007,2008],{"xmlns":596},[598,2009,2010,2015],{},[601,2011,2012],{},[604,2013,2014],{},"5832",[608,2016,2014],{"encoding":610},[585,2018,2020],{"className":2019,"ariaHidden":615},[614],[585,2021,2023,2026],{"className":2022},[619],[585,2024],{"className":2025,"style":624},[623],[585,2027,2014],{"className":2028},[628],":",[578,2031,2032,2211,2329,2447,2582],{},[581,2033,2034,2035,2153,2154,2182,2183,1143],{},"Quersumme ",[585,2036,2038,2069],{"className":2037},[588],[585,2039,2041],{"className":2040},[592],[594,2042,2043],{"xmlns":596},[598,2044,2045,2066],{},[601,2046,2047,2049,2051,2053,2055,2057,2059,2061,2063],{},[604,2048,738],{},[646,2050,1490],{},[604,2052,665],{},[646,2054,1490],{},[604,2056,1172],{},[646,2058,1490],{},[604,2060,606],{},[646,2062,1614],{},[604,2064,2065],{},"18",[608,2067,2068],{"encoding":610},"5 + 8 + 3 + 2 = 18",[585,2070,2072,2090,2108,2126,2144],{"className":2071,"ariaHidden":615},[614],[585,2073,2075,2078,2081,2084,2087],{"className":2074},[619],[585,2076],{"className":2077,"style":1511},[623],[585,2079,738],{"className":2080},[628],[585,2082],{"className":2083,"style":1521},[689],[585,2085,1490],{"className":2086},[1525],[585,2088],{"className":2089,"style":1521},[689],[585,2091,2093,2096,2099,2102,2105],{"className":2092},[619],[585,2094],{"className":2095,"style":1511},[623],[585,2097,665],{"className":2098},[628],[585,2100],{"className":2101,"style":1521},[689],[585,2103,1490],{"className":2104},[1525],[585,2106],{"className":2107,"style":1521},[689],[585,2109,2111,2114,2117,2120,2123],{"className":2110},[619],[585,2112],{"className":2113,"style":1511},[623],[585,2115,1172],{"className":2116},[628],[585,2118],{"className":2119,"style":1521},[689],[585,2121,1490],{"className":2122},[1525],[585,2124],{"className":2125,"style":1521},[689],[585,2127,2129,2132,2135,2138,2141],{"className":2128},[619],[585,2130],{"className":2131,"style":624},[623],[585,2133,606],{"className":2134},[628],[585,2136],{"className":2137,"style":1770},[689],[585,2139,1614],{"className":2140},[1774],[585,2142],{"className":2143,"style":1770},[689],[585,2145,2147,2150],{"className":2146},[619],[585,2148],{"className":2149,"style":624},[623],[585,2151,2065],{"className":2152},[628],", also durch ",[585,2155,2157,2170],{"className":2156},[588],[585,2158,2160],{"className":2159},[592],[594,2161,2162],{"xmlns":596},[598,2163,2164,2168],{},[601,2165,2166],{},[604,2167,1172],{},[608,2169,1172],{"encoding":610},[585,2171,2173],{"className":2172,"ariaHidden":615},[614],[585,2174,2176,2179],{"className":2175},[619],[585,2177],{"className":2178,"style":624},[623],[585,2180,1172],{"className":2181},[628]," und durch ",[585,2184,2186,2199],{"className":2185},[588],[585,2187,2189],{"className":2188},[592],[594,2190,2191],{"xmlns":596},[598,2192,2193,2197],{},[601,2194,2195],{},[604,2196,1232],{},[608,2198,1232],{"encoding":610},[585,2200,2202],{"className":2201,"ariaHidden":615},[614],[585,2203,2205,2208],{"className":2204},[619],[585,2206],{"className":2207,"style":624},[623],[585,2209,1232],{"className":2210},[628],[581,2212,2213,2214,2153,2242,2270,2271,2299,2300,2328],{},"Letzte Ziffer ",[585,2215,2217,2230],{"className":2216},[588],[585,2218,2220],{"className":2219},[592],[594,2221,2222],{"xmlns":596},[598,2223,2224,2228],{},[601,2225,2226],{},[604,2227,606],{},[608,2229,606],{"encoding":610},[585,2231,2233],{"className":2232,"ariaHidden":615},[614],[585,2234,2236,2239],{"className":2235},[619],[585,2237],{"className":2238,"style":624},[623],[585,2240,606],{"className":2241},[628],[585,2243,2245,2258],{"className":2244},[588],[585,2246,2248],{"className":2247},[592],[594,2249,2250],{"xmlns":596},[598,2251,2252,2256],{},[601,2253,2254],{},[604,2255,606],{},[608,2257,606],{"encoding":610},[585,2259,2261],{"className":2260,"ariaHidden":615},[614],[585,2262,2264,2267],{"className":2263},[619],[585,2265],{"className":2266,"style":624},[623],[585,2268,606],{"className":2269},[628]," teilbar, und zusammen mit der ",[585,2272,2274,2287],{"className":2273},[588],[585,2275,2277],{"className":2276},[592],[594,2278,2279],{"xmlns":596},[598,2280,2281,2285],{},[601,2282,2283],{},[604,2284,1172],{},[608,2286,1172],{"encoding":610},[585,2288,2290],{"className":2289,"ariaHidden":615},[614],[585,2291,2293,2296],{"className":2292},[619],[585,2294],{"className":2295,"style":624},[623],[585,2297,1172],{"className":2298},[628]," auch durch ",[585,2301,2303,2316],{"className":2302},[588],[585,2304,2306],{"className":2305},[592],[594,2307,2308],{"xmlns":596},[598,2309,2310,2314],{},[601,2311,2312],{},[604,2313,660],{},[608,2315,660],{"encoding":610},[585,2317,2319],{"className":2318,"ariaHidden":615},[614],[585,2320,2322,2325],{"className":2321},[619],[585,2323],{"className":2324,"style":624},[623],[585,2326,660],{"className":2327},[628],".",[581,2330,2331,2332,2361,2362,2390,2391,1342,2419,1143],{},"Letzte zwei Ziffern ",[585,2333,2335,2349],{"className":2334},[588],[585,2336,2338],{"className":2337},[592],[594,2339,2340],{"xmlns":596},[598,2341,2342,2347],{},[601,2343,2344],{},[604,2345,2346],{},"32",[608,2348,2346],{"encoding":610},[585,2350,2352],{"className":2351,"ariaHidden":615},[614],[585,2353,2355,2358],{"className":2354},[619],[585,2356],{"className":2357,"style":624},[623],[585,2359,2346],{"className":2360},[628]," sind durch ",[585,2363,2365,2378],{"className":2364},[588],[585,2366,2368],{"className":2367},[592],[594,2369,2370],{"xmlns":596},[598,2371,2372,2376],{},[601,2373,2374],{},[604,2375,655],{},[608,2377,655],{"encoding":610},[585,2379,2381],{"className":2380,"ariaHidden":615},[614],[585,2382,2384,2387],{"className":2383},[619],[585,2385],{"className":2386,"style":624},[623],[585,2388,655],{"className":2389},[628]," teilbar, also ist ",[585,2392,2394,2407],{"className":2393},[588],[585,2395,2397],{"className":2396},[592],[594,2398,2399],{"xmlns":596},[598,2400,2401,2405],{},[601,2402,2403],{},[604,2404,2014],{},[608,2406,2014],{"encoding":610},[585,2408,2410],{"className":2409,"ariaHidden":615},[614],[585,2411,2413,2416],{"className":2412},[619],[585,2414],{"className":2415,"style":624},[623],[585,2417,2014],{"className":2418},[628],[585,2420,2422,2435],{"className":2421},[588],[585,2423,2425],{"className":2424},[592],[594,2426,2427],{"xmlns":596},[598,2428,2429,2433],{},[601,2430,2431],{},[604,2432,655],{},[608,2434,655],{"encoding":610},[585,2436,2438],{"className":2437,"ariaHidden":615},[614],[585,2439,2441,2444],{"className":2440},[619],[585,2442],{"className":2443,"style":624},[623],[585,2445,655],{"className":2446},[628],[581,2448,2449,2450,2525,2526,1342,2554,1143],{},"Letzte drei Ziffern ",[585,2451,2453,2477],{"className":2452},[588],[585,2454,2456],{"className":2455},[592],[594,2457,2458],{"xmlns":596},[598,2459,2460,2474],{},[601,2461,2462,2465,2467,2469,2471],{},[604,2463,2464],{},"832",[646,2466,1614],{},[604,2468,665],{},[646,2470,1632],{},[604,2472,2473],{},"104",[608,2475,2476],{"encoding":610},"832 = 8 \\cdot 104",[585,2478,2480,2498,2516],{"className":2479,"ariaHidden":615},[614],[585,2481,2483,2486,2489,2492,2495],{"className":2482},[619],[585,2484],{"className":2485,"style":624},[623],[585,2487,2464],{"className":2488},[628],[585,2490],{"className":2491,"style":1770},[689],[585,2493,1614],{"className":2494},[1774],[585,2496],{"className":2497,"style":1770},[689],[585,2499,2501,2504,2507,2510,2513],{"className":2500},[619],[585,2502],{"className":2503,"style":624},[623],[585,2505,665],{"className":2506},[628],[585,2508],{"className":2509,"style":1521},[689],[585,2511,1632],{"className":2512},[1525],[585,2514],{"className":2515,"style":1521},[689],[585,2517,2519,2522],{"className":2518},[619],[585,2520],{"className":2521,"style":624},[623],[585,2523,2473],{"className":2524},[628],", also ist ",[585,2527,2529,2542],{"className":2528},[588],[585,2530,2532],{"className":2531},[592],[594,2533,2534],{"xmlns":596},[598,2535,2536,2540],{},[601,2537,2538],{},[604,2539,2014],{},[608,2541,2014],{"encoding":610},[585,2543,2545],{"className":2544,"ariaHidden":615},[614],[585,2546,2548,2551],{"className":2547},[619],[585,2549],{"className":2550,"style":624},[623],[585,2552,2014],{"className":2553},[628],[585,2555,2557,2570],{"className":2556},[588],[585,2558,2560],{"className":2559},[592],[594,2561,2562],{"xmlns":596},[598,2563,2564,2568],{},[601,2565,2566],{},[604,2567,665],{},[608,2569,665],{"encoding":610},[585,2571,2573],{"className":2572,"ariaHidden":615},[614],[585,2574,2576,2579],{"className":2575},[619],[585,2577],{"className":2578,"style":624},[623],[585,2580,665],{"className":2581},[628],[581,2583,2584,2585,2613,2614,2642,2643,2671,2672,2700],{},"Letzte Ziffer ist weder ",[585,2586,2588,2601],{"className":2587},[588],[585,2589,2591],{"className":2590},[592],[594,2592,2593],{"xmlns":596},[598,2594,2595,2599],{},[601,2596,2597],{},[604,2598,644],{},[608,2600,644],{"encoding":610},[585,2602,2604],{"className":2603,"ariaHidden":615},[614],[585,2605,2607,2610],{"className":2606},[619],[585,2608],{"className":2609,"style":624},[623],[585,2611,644],{"className":2612},[628]," noch ",[585,2615,2617,2630],{"className":2616},[588],[585,2618,2620],{"className":2619},[592],[594,2621,2622],{"xmlns":596},[598,2623,2624,2628],{},[601,2625,2626],{},[604,2627,738],{},[608,2629,738],{"encoding":610},[585,2631,2633],{"className":2632,"ariaHidden":615},[614],[585,2634,2636,2639],{"className":2635},[619],[585,2637],{"className":2638,"style":624},[623],[585,2640,738],{"className":2641},[628],", also nicht durch ",[585,2644,2646,2659],{"className":2645},[588],[585,2647,2649],{"className":2648},[592],[594,2650,2651],{"xmlns":596},[598,2652,2653,2657],{},[601,2654,2655],{},[604,2656,738],{},[608,2658,738],{"encoding":610},[585,2660,2662],{"className":2661,"ariaHidden":615},[614],[585,2663,2665,2668],{"className":2664},[619],[585,2666],{"className":2667,"style":624},[623],[585,2669,738],{"className":2670},[628]," teilbar (Rest ",[585,2673,2675,2688],{"className":2674},[588],[585,2676,2678],{"className":2677},[592],[594,2679,2680],{"xmlns":596},[598,2681,2682,2686],{},[601,2683,2684],{},[604,2685,606],{},[608,2687,606],{"encoding":610},[585,2689,2691],{"className":2690,"ariaHidden":615},[614],[585,2692,2694,2697],{"className":2693},[619],[585,2695],{"className":2696,"style":624},[623],[585,2698,606],{"className":2699},[628],").",[564,2702,1999,2703,2029],{},[585,2704,2706,2720],{"className":2705},[588],[585,2707,2709],{"className":2708},[592],[594,2710,2711],{"xmlns":596},[598,2712,2713,2718],{},[601,2714,2715],{},[604,2716,2717],{},"1245",[608,2719,2717],{"encoding":610},[585,2721,2723],{"className":2722,"ariaHidden":615},[614],[585,2724,2726,2729],{"className":2725},[619],[585,2727],{"className":2728,"style":624},[623],[585,2730,2717],{"className":2731},[628],[578,2733,2734,3087],{},[581,2735,2034,2736,2855,2856,2884,2885,2913,2914,2942,2943,2971,2972,3000,3001,3029,3030,2971,3058,3086],{},[585,2737,2739,2771],{"className":2738},[588],[585,2740,2742],{"className":2741},[592],[594,2743,2744],{"xmlns":596},[598,2745,2746,2768],{},[601,2747,2748,2751,2753,2755,2757,2759,2761,2763,2765],{},[604,2749,2750],{},"1",[646,2752,1490],{},[604,2754,606],{},[646,2756,1490],{},[604,2758,655],{},[646,2760,1490],{},[604,2762,738],{},[646,2764,1614],{},[604,2766,2767],{},"12",[608,2769,2770],{"encoding":610},"1 + 2 + 4 + 5 = 12",[585,2772,2774,2792,2810,2828,2846],{"className":2773,"ariaHidden":615},[614],[585,2775,2777,2780,2783,2786,2789],{"className":2776},[619],[585,2778],{"className":2779,"style":1511},[623],[585,2781,2750],{"className":2782},[628],[585,2784],{"className":2785,"style":1521},[689],[585,2787,1490],{"className":2788},[1525],[585,2790],{"className":2791,"style":1521},[689],[585,2793,2795,2798,2801,2804,2807],{"className":2794},[619],[585,2796],{"className":2797,"style":1511},[623],[585,2799,606],{"className":2800},[628],[585,2802],{"className":2803,"style":1521},[689],[585,2805,1490],{"className":2806},[1525],[585,2808],{"className":2809,"style":1521},[689],[585,2811,2813,2816,2819,2822,2825],{"className":2812},[619],[585,2814],{"className":2815,"style":1511},[623],[585,2817,655],{"className":2818},[628],[585,2820],{"className":2821,"style":1521},[689],[585,2823,1490],{"className":2824},[1525],[585,2826],{"className":2827,"style":1521},[689],[585,2829,2831,2834,2837,2840,2843],{"className":2830},[619],[585,2832],{"className":2833,"style":624},[623],[585,2835,738],{"className":2836},[628],[585,2838],{"className":2839,"style":1770},[689],[585,2841,1614],{"className":2842},[1774],[585,2844],{"className":2845,"style":1770},[689],[585,2847,2849,2852],{"className":2848},[619],[585,2850],{"className":2851,"style":624},[623],[585,2853,2767],{"className":2854},[628],": durch ",[585,2857,2859,2872],{"className":2858},[588],[585,2860,2862],{"className":2861},[592],[594,2863,2864],{"xmlns":596},[598,2865,2866,2870],{},[601,2867,2868],{},[604,2869,1172],{},[608,2871,1172],{"encoding":610},[585,2873,2875],{"className":2874,"ariaHidden":615},[614],[585,2876,2878,2881],{"className":2877},[619],[585,2879],{"className":2880,"style":624},[623],[585,2882,1172],{"className":2883},[628]," teilbar, aber nicht durch ",[585,2886,2888,2901],{"className":2887},[588],[585,2889,2891],{"className":2890},[592],[594,2892,2893],{"xmlns":596},[598,2894,2895,2899],{},[601,2896,2897],{},[604,2898,1232],{},[608,2900,1232],{"encoding":610},[585,2902,2904],{"className":2903,"ariaHidden":615},[614],[585,2905,2907,2910],{"className":2906},[619],[585,2908],{"className":2909,"style":624},[623],[585,2911,1232],{"className":2912},[628],". Der Rest bei ",[585,2915,2917,2930],{"className":2916},[588],[585,2918,2920],{"className":2919},[592],[594,2921,2922],{"xmlns":596},[598,2923,2924,2928],{},[601,2925,2926],{},[604,2927,1232],{},[608,2929,1232],{"encoding":610},[585,2931,2933],{"className":2932,"ariaHidden":615},[614],[585,2934,2936,2939],{"className":2935},[619],[585,2937],{"className":2938,"style":624},[623],[585,2940,1232],{"className":2941},[628]," ist derselbe wie bei der Quersumme: ",[585,2944,2946,2959],{"className":2945},[588],[585,2947,2949],{"className":2948},[592],[594,2950,2951],{"xmlns":596},[598,2952,2953,2957],{},[601,2954,2955],{},[604,2956,2767],{},[608,2958,2767],{"encoding":610},[585,2960,2962],{"className":2961,"ariaHidden":615},[614],[585,2963,2965,2968],{"className":2964},[619],[585,2966],{"className":2967,"style":624},[623],[585,2969,2767],{"className":2970},[628]," geteilt durch ",[585,2973,2975,2988],{"className":2974},[588],[585,2976,2978],{"className":2977},[592],[594,2979,2980],{"xmlns":596},[598,2981,2982,2986],{},[601,2983,2984],{},[604,2985,1232],{},[608,2987,1232],{"encoding":610},[585,2989,2991],{"className":2990,"ariaHidden":615},[614],[585,2992,2994,2997],{"className":2993},[619],[585,2995],{"className":2996,"style":624},[623],[585,2998,1232],{"className":2999},[628]," lässt Rest ",[585,3002,3004,3017],{"className":3003},[588],[585,3005,3007],{"className":3006},[592],[594,3008,3009],{"xmlns":596},[598,3010,3011,3015],{},[601,3012,3013],{},[604,3014,1172],{},[608,3016,1172],{"encoding":610},[585,3018,3020],{"className":3019,"ariaHidden":615},[614],[585,3021,3023,3026],{"className":3022},[619],[585,3024],{"className":3025,"style":624},[623],[585,3027,1172],{"className":3028},[628],", und ",[585,3031,3033,3046],{"className":3032},[588],[585,3034,3036],{"className":3035},[592],[594,3037,3038],{"xmlns":596},[598,3039,3040,3044],{},[601,3041,3042],{},[604,3043,2717],{},[608,3045,2717],{"encoding":610},[585,3047,3049],{"className":3048,"ariaHidden":615},[614],[585,3050,3052,3055],{"className":3051},[619],[585,3053],{"className":3054,"style":624},[623],[585,3056,2717],{"className":3057},[628],[585,3059,3061,3074],{"className":3060},[588],[585,3062,3064],{"className":3063},[592],[594,3065,3066],{"xmlns":596},[598,3067,3068,3072],{},[601,3069,3070],{},[604,3071,1232],{},[608,3073,1232],{"encoding":610},[585,3075,3077],{"className":3076,"ariaHidden":615},[614],[585,3078,3080,3083],{"className":3079},[619],[585,3081],{"className":3082,"style":624},[623],[585,3084,1232],{"className":3085},[628]," auch.",[581,3088,2213,3089,2855,3117,2884,3145,2328],{},[585,3090,3092,3105],{"className":3091},[588],[585,3093,3095],{"className":3094},[592],[594,3096,3097],{"xmlns":596},[598,3098,3099,3103],{},[601,3100,3101],{},[604,3102,738],{},[608,3104,738],{"encoding":610},[585,3106,3108],{"className":3107,"ariaHidden":615},[614],[585,3109,3111,3114],{"className":3110},[619],[585,3112],{"className":3113,"style":624},[623],[585,3115,738],{"className":3116},[628],[585,3118,3120,3133],{"className":3119},[588],[585,3121,3123],{"className":3122},[592],[594,3124,3125],{"xmlns":596},[598,3126,3127,3131],{},[601,3128,3129],{},[604,3130,738],{},[608,3132,738],{"encoding":610},[585,3134,3136],{"className":3135,"ariaHidden":615},[614],[585,3137,3139,3142],{"className":3138},[619],[585,3140],{"className":3141,"style":624},[623],[585,3143,738],{"className":3144},[628],[585,3146,3148,3161],{"className":3147},[588],[585,3149,3151],{"className":3150},[592],[594,3152,3153],{"xmlns":596},[598,3154,3155,3159],{},[601,3156,3157],{},[604,3158,606],{},[608,3160,606],{"encoding":610},[585,3162,3164],{"className":3163,"ariaHidden":615},[614],[585,3165,3167,3170],{"className":3166},[619],[585,3168],{"className":3169,"style":624},[623],[585,3171,606],{"className":3172},[628],[559,3174,3176],{"id":3175},"typische-fehler","Typische Fehler",[578,3178,3179,3418,3563],{},[581,3180,3181,3182,3210,3211,3240,3241,3270,3271,3299,3300,3328,3329,3357,3358,3387,3388,3417],{},"Bei der ",[585,3183,3185,3198],{"className":3184},[588],[585,3186,3188],{"className":3187},[592],[594,3189,3190],{"xmlns":596},[598,3191,3192,3196],{},[601,3193,3194],{},[604,3195,655],{},[608,3197,655],{"encoding":610},[585,3199,3201],{"className":3200,"ariaHidden":615},[614],[585,3202,3204,3207],{"className":3203},[619],[585,3205],{"className":3206,"style":624},[623],[585,3208,655],{"className":3209},[628]," nur auf die letzte Ziffer schauen. ",[585,3212,3214,3228],{"className":3213},[588],[585,3215,3217],{"className":3216},[592],[594,3218,3219],{"xmlns":596},[598,3220,3221,3226],{},[601,3222,3223],{},[604,3224,3225],{},"316",[608,3227,3225],{"encoding":610},[585,3229,3231],{"className":3230,"ariaHidden":615},[614],[585,3232,3234,3237],{"className":3233},[619],[585,3235],{"className":3236,"style":624},[623],[585,3238,3225],{"className":3239},[628]," und ",[585,3242,3244,3258],{"className":3243},[588],[585,3245,3247],{"className":3246},[592],[594,3248,3249],{"xmlns":596},[598,3250,3251,3256],{},[601,3252,3253],{},[604,3254,3255],{},"326",[608,3257,3255],{"encoding":610},[585,3259,3261],{"className":3260,"ariaHidden":615},[614],[585,3262,3264,3267],{"className":3263},[619],[585,3265],{"className":3266,"style":624},[623],[585,3268,3255],{"className":3269},[628]," enden beide auf ",[585,3272,3274,3287],{"className":3273},[588],[585,3275,3277],{"className":3276},[592],[594,3278,3279],{"xmlns":596},[598,3280,3281,3285],{},[601,3282,3283],{},[604,3284,660],{},[608,3286,660],{"encoding":610},[585,3288,3290],{"className":3289,"ariaHidden":615},[614],[585,3291,3293,3296],{"className":3292},[619],[585,3294],{"className":3295,"style":624},[623],[585,3297,660],{"className":3298},[628],", aber nur ",[585,3301,3303,3316],{"className":3302},[588],[585,3304,3306],{"className":3305},[592],[594,3307,3308],{"xmlns":596},[598,3309,3310,3314],{},[601,3311,3312],{},[604,3313,3225],{},[608,3315,3225],{"encoding":610},[585,3317,3319],{"className":3318,"ariaHidden":615},[614],[585,3320,3322,3325],{"className":3321},[619],[585,3323],{"className":3324,"style":624},[623],[585,3326,3225],{"className":3327},[628]," ist durch ",[585,3330,3332,3345],{"className":3331},[588],[585,3333,3335],{"className":3334},[592],[594,3336,3337],{"xmlns":596},[598,3338,3339,3343],{},[601,3340,3341],{},[604,3342,655],{},[608,3344,655],{"encoding":610},[585,3346,3348],{"className":3347,"ariaHidden":615},[614],[585,3349,3351,3354],{"className":3350},[619],[585,3352],{"className":3353,"style":624},[623],[585,3355,655],{"className":3356},[628]," teilbar (",[585,3359,3361,3375],{"className":3360},[588],[585,3362,3364],{"className":3363},[592],[594,3365,3366],{"xmlns":596},[598,3367,3368,3373],{},[601,3369,3370],{},[604,3371,3372],{},"16",[608,3374,3372],{"encoding":610},[585,3376,3378],{"className":3377,"ariaHidden":615},[614],[585,3379,3381,3384],{"className":3380},[619],[585,3382],{"className":3383,"style":624},[623],[585,3385,3372],{"className":3386},[628]," ja, ",[585,3389,3391,3405],{"className":3390},[588],[585,3392,3394],{"className":3393},[592],[594,3395,3396],{"xmlns":596},[598,3397,3398,3403],{},[601,3399,3400],{},[604,3401,3402],{},"26",[608,3404,3402],{"encoding":610},[585,3406,3408],{"className":3407,"ariaHidden":615},[614],[585,3409,3411,3414],{"className":3410},[619],[585,3412],{"className":3413,"style":624},[623],[585,3415,3402],{"className":3416},[628]," nein).",[581,3419,3420,3421,3240,3449,3477,3478,995,3506,782,3534,2328],{},"Die Quersummenregel für andere Zahlen verwenden. Sie gilt nur für ",[585,3422,3424,3437],{"className":3423},[588],[585,3425,3427],{"className":3426},[592],[594,3428,3429],{"xmlns":596},[598,3430,3431,3435],{},[601,3432,3433],{},[604,3434,1172],{},[608,3436,1172],{"encoding":610},[585,3438,3440],{"className":3439,"ariaHidden":615},[614],[585,3441,3443,3446],{"className":3442},[619],[585,3444],{"className":3445,"style":624},[623],[585,3447,1172],{"className":3448},[628],[585,3450,3452,3465],{"className":3451},[588],[585,3453,3455],{"className":3454},[592],[594,3456,3457],{"xmlns":596},[598,3458,3459,3463],{},[601,3460,3461],{},[604,3462,1232],{},[608,3464,1232],{"encoding":610},[585,3466,3468],{"className":3467,"ariaHidden":615},[614],[585,3469,3471,3474],{"className":3470},[619],[585,3472],{"className":3473,"style":624},[623],[585,3475,1232],{"className":3476},[628],", nicht für ",[585,3479,3481,3494],{"className":3480},[588],[585,3482,3484],{"className":3483},[592],[594,3485,3486],{"xmlns":596},[598,3487,3488,3492],{},[601,3489,3490],{},[604,3491,655],{},[608,3493,655],{"encoding":610},[585,3495,3497],{"className":3496,"ariaHidden":615},[614],[585,3498,3500,3503],{"className":3499},[619],[585,3501],{"className":3502,"style":624},[623],[585,3504,655],{"className":3505},[628],[585,3507,3509,3522],{"className":3508},[588],[585,3510,3512],{"className":3511},[592],[594,3513,3514],{"xmlns":596},[598,3515,3516,3520],{},[601,3517,3518],{},[604,3519,660],{},[608,3521,660],{"encoding":610},[585,3523,3525],{"className":3524,"ariaHidden":615},[614],[585,3526,3528,3531],{"className":3527},[619],[585,3529],{"className":3530,"style":624},[623],[585,3532,660],{"className":3533},[628],[585,3535,3537,3551],{"className":3536},[588],[585,3538,3540],{"className":3539},[592],[594,3541,3542],{"xmlns":596},[598,3543,3544,3549],{},[601,3545,3546],{},[604,3547,3548],{},"7",[608,3550,3548],{"encoding":610},[585,3552,3554],{"className":3553,"ariaHidden":615},[614],[585,3555,3557,3560],{"className":3556},[619],[585,3558],{"className":3559,"style":624},[623],[585,3561,3548],{"className":3562},[628],[581,3564,3565,3566,3328,3594,2182,3622,2884,3650,3679,3680,3240,3708,3736,3737,2328],{},"Teilbarkeiten einfach multiplizieren. ",[585,3567,3569,3582],{"className":3568},[588],[585,3570,3572],{"className":3571},[592],[594,3573,3574],{"xmlns":596},[598,3575,3576,3580],{},[601,3577,3578],{},[604,3579,2767],{},[608,3581,2767],{"encoding":610},[585,3583,3585],{"className":3584,"ariaHidden":615},[614],[585,3586,3588,3591],{"className":3587},[619],[585,3589],{"className":3590,"style":624},[623],[585,3592,2767],{"className":3593},[628],[585,3595,3597,3610],{"className":3596},[588],[585,3598,3600],{"className":3599},[592],[594,3601,3602],{"xmlns":596},[598,3603,3604,3608],{},[601,3605,3606],{},[604,3607,655],{},[608,3609,655],{"encoding":610},[585,3611,3613],{"className":3612,"ariaHidden":615},[614],[585,3614,3616,3619],{"className":3615},[619],[585,3617],{"className":3618,"style":624},[623],[585,3620,655],{"className":3621},[628],[585,3623,3625,3638],{"className":3624},[588],[585,3626,3628],{"className":3627},[592],[594,3629,3630],{"xmlns":596},[598,3631,3632,3636],{},[601,3633,3634],{},[604,3635,660],{},[608,3637,660],{"encoding":610},[585,3639,3641],{"className":3640,"ariaHidden":615},[614],[585,3642,3644,3647],{"className":3643},[619],[585,3645],{"className":3646,"style":624},[623],[585,3648,660],{"className":3649},[628],[585,3651,3653,3667],{"className":3652},[588],[585,3654,3656],{"className":3655},[592],[594,3657,3658],{"xmlns":596},[598,3659,3660,3665],{},[601,3661,3662],{},[604,3663,3664],{},"24",[608,3666,3664],{"encoding":610},[585,3668,3670],{"className":3669,"ariaHidden":615},[614],[585,3671,3673,3676],{"className":3672},[619],[585,3674],{"className":3675,"style":624},[623],[585,3677,3664],{"className":3678},[628],". Das Kombinieren klappt nur mit Zahlen ohne gemeinsamen Teiler, wie ",[585,3681,3683,3696],{"className":3682},[588],[585,3684,3686],{"className":3685},[592],[594,3687,3688],{"xmlns":596},[598,3689,3690,3694],{},[601,3691,3692],{},[604,3693,606],{},[608,3695,606],{"encoding":610},[585,3697,3699],{"className":3698,"ariaHidden":615},[614],[585,3700,3702,3705],{"className":3701},[619],[585,3703],{"className":3704,"style":624},[623],[585,3706,606],{"className":3707},[628],[585,3709,3711,3724],{"className":3710},[588],[585,3712,3714],{"className":3713},[592],[594,3715,3716],{"xmlns":596},[598,3717,3718,3722],{},[601,3719,3720],{},[604,3721,1172],{},[608,3723,1172],{"encoding":610},[585,3725,3727],{"className":3726,"ariaHidden":615},[614],[585,3728,3730,3733],{"className":3729},[619],[585,3731],{"className":3732,"style":624},[623],[585,3734,1172],{"className":3735},[628]," bei der ",[585,3738,3740,3753],{"className":3739},[588],[585,3741,3743],{"className":3742},[592],[594,3744,3745],{"xmlns":596},[598,3746,3747,3751],{},[601,3748,3749],{},[604,3750,660],{},[608,3752,660],{"encoding":610},[585,3754,3756],{"className":3755,"ariaHidden":615},[614],[585,3757,3759,3762],{"className":3758},[619],[585,3760],{"className":3761,"style":624},[623],[585,3763,660],{"className":3764},[628],{"title":3766,"searchDepth":3767,"depth":3767,"links":3768},"",2,[3769,3770,3771,3772],{"id":561,"depth":3767,"text":562},{"id":1374,"depth":3767,"text":1375},{"id":1995,"depth":3767,"text":1996},{"id":3175,"depth":3767,"text":3176},[3774,3777,3779,3781,3783,3785,3787,3789,3791,3793,3795,3797,3799,3801,3803,3805,3807,3809,3811,3813],{"lhs":3775,"rhs":3776},"100*a + 10*b + c - (a + b + c)","9*(11*a + b)",{"lhs":3778,"rhs":2065},"5 + 8 + 3 + 2",{"lhs":3780,"rhs":644},"mod(5832, 3)",{"lhs":3782,"rhs":644},"mod(5832, 9)",{"lhs":3784,"rhs":644},"mod(5832, 2)",{"lhs":3786,"rhs":644},"mod(32, 4)",{"lhs":3788,"rhs":644},"mod(5832, 4)",{"lhs":3790,"rhs":2473},"832\u002F8",{"lhs":3792,"rhs":644},"mod(5832, 8)",{"lhs":3794,"rhs":644},"mod(5832, 6)",{"lhs":3796,"rhs":606},"mod(5832, 5)",{"lhs":3798,"rhs":2767},"1 + 2 + 4 + 5",{"lhs":3800,"rhs":644},"mod(1245, 3)",{"lhs":3802,"rhs":1172},"mod(1245, 9)",{"lhs":3804,"rhs":1172},"mod(12, 9)",{"lhs":3806,"rhs":644},"mod(1245, 5)",{"lhs":3808,"rhs":2750},"mod(1245, 2)",{"lhs":3810,"rhs":644},"mod(316, 4)",{"lhs":3812,"rhs":606},"mod(326, 4)",{"lhs":3814,"rhs":2767},"mod(12, 24)","n \\in \\mathbb{N}","\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>\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","divisibility-rules","3 \\mid n \\iff 3 \\mid Q(n) \\qquad 9 \\mid n \\iff 9 \\mid Q(n)","\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>\u003Cmn>3\u003C\u002Fmn>\u003Cmo>∣\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmn>3\u003C\u002Fmn>\u003Cmo>∣\u003C\u002Fmo>\u003Cmi>Q\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmn>9\u003C\u002Fmn>\u003Cmo>∣\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmn>9\u003C\u002Fmn>\u003Cmo>∣\u003C\u002Fmo>\u003Cmi>Q\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">3 \\mid n \\iff 3 \\mid Q(n) \\qquad 9 \\mid n \\iff 9 \\mid Q(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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\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:0.549em;vertical-align:-0.024em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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>\u003Cspan 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