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und jeder gemeinsame Teiler von ",[573,1139,1141,1154],{"className":1140},[580],[573,1142,1144],{"className":1143},[584],[586,1145,1146],{"xmlns":588},[591,1147,1148,1152],{},[594,1149,1150],{},[597,1151,618],{},[665,1153,618],{"encoding":667},[573,1155,1157],{"className":1156,"ariaHidden":614},[672],[573,1158,1160,1163],{"className":1159},[676],[573,1161],{"className":1162,"style":977},[680],[573,1164,618],{"className":1165},[689,698],[573,1167,1169,1182],{"className":1168},[580],[573,1170,1172],{"className":1171},[584],[586,1173,1174],{"xmlns":588},[591,1175,1176,1180],{},[594,1177,1178],{},[597,1179,825],{},[665,1181,825],{"encoding":667},[573,1183,1185],{"className":1184,"ariaHidden":614},[672],[573,1186,1188,1191],{"className":1187},[676],[573,1189],{"className":1190,"style":838},[680],[573,1192,825],{"className":1193,"style":899},[689,698]," teilt auch ",[573,1196,1198,1211],{"className":1197},[580],[573,1199,1201],{"className":1200},[584],[586,1202,1203],{"xmlns":588},[591,1204,1205,1209],{},[594,1206,1207],{},[597,1208,611],{},[665,1210,611],{"encoding":667},[573,1212,1214],{"className":1213,"ariaHidden":614},[672],[573,1215,1217,1220],{"className":1216},[676],[573,1218],{"className":1219,"style":838},[680],[573,1221,611],{"className":1222},[689,698],". Beide Paare haben also dieselben gemeinsamen Teiler.",[564,1225,1226,1227,1279,1280,1332,1333,1362,1363],{},"Ablauf: Man teilt mit Rest, ersetzt ",[573,1228,1230,1252],{"className":1229},[580],[573,1231,1233],{"className":1232},[584],[586,1234,1235],{"xmlns":588},[591,1236,1237,1249],{},[594,1238,1239,1241,1243,1245,1247],{},[602,1240,608],{"stretchy":607},[597,1242,611],{},[602,1244,615],{"separator":614},[597,1246,618],{},[602,1248,621],{"stretchy":607},[665,1250,1251],{"encoding":667},"(a, b)",[573,1253,1255],{"className":1254,"ariaHidden":614},[672],[573,1256,1258,1261,1264,1267,1270,1273,1276],{"className":1257},[676],[573,1259],{"className":1260,"style":681},[680],[573,1262,608],{"className":1263},[694],[573,1265,611],{"className":1266},[689,698],[573,1268,615],{"className":1269},[702],[573,1271],{"className":1272,"style":707},[706],[573,1274,618],{"className":1275},[689,698],[573,1277,621],{"className":1278},[714]," durch ",[573,1281,1283,1305],{"className":1282},[580],[573,1284,1286],{"className":1285},[584],[586,1287,1288],{"xmlns":588},[591,1289,1290,1302],{},[594,1291,1292,1294,1296,1298,1300],{},[602,1293,608],{"stretchy":607},[597,1295,618],{},[602,1297,615],{"separator":614},[597,1299,825],{},[602,1301,621],{"stretchy":607},[665,1303,1304],{"encoding":667},"(b, r)",[573,1306,1308],{"className":1307,"ariaHidden":614},[672],[573,1309,1311,1314,1317,1320,1323,1326,1329],{"className":1310},[676],[573,1312],{"className":1313,"style":681},[680],[573,1315,608],{"className":1316},[694],[573,1318,618],{"className":1319},[689,698],[573,1321,615],{"className":1322},[702],[573,1324],{"className":1325,"style":707},[706],[573,1327,825],{"className":1328,"style":899},[689,698],[573,1330,621],{"className":1331},[714]," und wiederholt das. Die Reste werden echt kleiner, also erreicht man nach endlich vielen Schritten den Rest ",[573,1334,1336,1349],{"className":1335},[580],[573,1337,1339],{"className":1338},[584],[586,1340,1341],{"xmlns":588},[591,1342,1343,1347],{},[594,1344,1345],{},[914,1346,916],{},[665,1348,916],{"encoding":667},[573,1350,1352],{"className":1351,"ariaHidden":614},[672],[573,1353,1355,1359],{"className":1354},[676],[573,1356],{"className":1357,"style":1358},[680],"height:0.6444em;",[573,1360,916],{"className":1361},[689],". ",[568,1364,1365],{},"Der letzte von null verschiedene Rest ist der ggT.",[564,1367,1368],{},"Der Algorithmus ist sehr schnell: Die Zahl der Schritte wächst nur logarithmisch mit der Größe der Zahlen (Satz von Lamé). Am langsamsten ist er bei aufeinanderfolgenden Fibonacci-Zahlen.",[559,1370,1372],{"id":1371},"beispiele","Beispiele",[564,1374,1375,1439],{},[573,1376,1378,1406],{"className":1377},[580],[573,1379,1381],{"className":1380},[584],[586,1382,1383],{"xmlns":588},[591,1384,1385,1403],{},[594,1386,1387,1389,1391,1393,1396,1398,1401],{},[597,1388,600],{"mathvariant":599},[602,1390,604],{},[602,1392,608],{"stretchy":607},[914,1394,1395],{},"1071",[602,1397,615],{"separator":614},[914,1399,1400],{},"462",[602,1402,621],{"stretchy":607},[665,1404,1405],{"encoding":667},"\\operatorname{ggT}(1071, 462)",[573,1407,1409],{"className":1408,"ariaHidden":614},[672],[573,1410,1412,1415,1421,1424,1427,1430,1433,1436],{"className":1411},[676],[573,1413],{"className":1414,"style":681},[680],[573,1416,1418],{"className":1417},[685],[573,1419,600],{"className":1420},[689,690],[573,1422,608],{"className":1423},[694],[573,1425,1395],{"className":1426},[689],[573,1428,615],{"className":1429},[702],[573,1431],{"className":1432,"style":707},[706],[573,1434,1400],{"className":1435},[689],[573,1437,621],{"className":1438},[714],":",[573,1441,1443],{"className":1442},[576],[573,1444,1446,1554],{"className":1445},[580],[573,1447,1449],{"className":1448},[584],[586,1450,1451],{"xmlns":588,"display":589},[591,1452,1453,1551],{},[1454,1455,1459,1492,1522],"mtable",{"rowspacing":1456,"columnalign":1457,"columnspacing":1458},"0.25em","right left","0em",[1460,1461,1462,1470],"mtr",{},[1463,1464,1465],"mtd",{},[1466,1467,1468],"mstyle",{"scriptlevel":916,"displaystyle":614},[914,1469,1395],{},[1463,1471,1472],{},[1466,1473,1474],{"scriptlevel":916,"displaystyle":614},[594,1475,1476,1478,1480,1483,1485,1487,1489],{},[594,1477],{},[602,1479,624],{},[914,1481,1482],{},"2",[602,1484,817],{},[914,1486,1400],{},[602,1488,822],{},[914,1490,1491],{},"147",[1460,1493,1494,1500],{},[1463,1495,1496],{},[1466,1497,1498],{"scriptlevel":916,"displaystyle":614},[914,1499,1400],{},[1463,1501,1502],{},[1466,1503,1504],{"scriptlevel":916,"displaystyle":614},[594,1505,1506,1508,1510,1513,1515,1517,1519],{},[594,1507],{},[602,1509,624],{},[914,1511,1512],{},"3",[602,1514,817],{},[914,1516,1491],{},[602,1518,822],{},[914,1520,1521],{},"21",[1460,1523,1524,1530],{},[1463,1525,1526],{},[1466,1527,1528],{"scriptlevel":916,"displaystyle":614},[914,1529,1491],{},[1463,1531,1532],{},[1466,1533,1534],{"scriptlevel":916,"displaystyle":614},[594,1535,1536,1538,1540,1543,1545,1547,1549],{},[594,1537],{},[602,1539,624],{},[914,1541,1542],{},"7",[602,1544,817],{},[914,1546,1521],{},[602,1548,822],{},[914,1550,916],{},[665,1552,1553],{"encoding":667},"\\begin{aligned}\n1071 &= 2 \\cdot 462 + 147 \\\\\n462 &= 3 \\cdot 147 + 21 \\\\\n147 &= 7 \\cdot 21 + 0\n\\end{aligned}",[573,1555,1557],{"className":1556,"ariaHidden":614},[672],[573,1558,1560,1564],{"className":1559},[676],[573,1561],{"className":1562,"style":1563},[680],"height:4.2em;vertical-align:-1.85em;",[573,1565,1567],{"className":1566},[689],[573,1568,1570,1640],{"className":1569},[1454],[573,1571,1574],{"className":1572},[1573],"col-align-r",[573,1575,1579,1631],{"className":1576},[1577,1578],"vlist-t","vlist-t2",[573,1580,1583,1626],{"className":1581},[1582],"vlist-r",[573,1584,1588,1602,1614],{"className":1585,"style":1587},[1586],"vlist","height:2.35em;",[573,1589,1591,1596],{"style":1590},"top:-4.51em;",[573,1592],{"className":1593,"style":1595},[1594],"pstrut","height:3em;",[573,1597,1599],{"className":1598},[689],[573,1600,1395],{"className":1601},[689],[573,1603,1605,1608],{"style":1604},"top:-3.01em;",[573,1606],{"className":1607,"style":1595},[1594],[573,1609,1611],{"className":1610},[689],[573,1612,1400],{"className":1613},[689],[573,1615,1617,1620],{"style":1616},"top:-1.51em;",[573,1618],{"className":1619,"style":1595},[1594],[573,1621,1623],{"className":1622},[689],[573,1624,1491],{"className":1625},[689],[573,1627,1630],{"className":1628},[1629],"vlist-s","​",[573,1632,1634],{"className":1633},[1582],[573,1635,1638],{"className":1636,"style":1637},[1586],"height:1.85em;",[573,1639],{},[573,1641,1644],{"className":1642},[1643],"col-align-l",[573,1645,1647,1797],{"className":1646},[1577,1578],[573,1648,1650,1794],{"className":1649},[1582],[573,1651,1653,1700,1747],{"className":1652,"style":1587},[1586],[573,1654,1655,1658],{"style":1590},[573,1656],{"className":1657,"style":1595},[1594],[573,1659,1661,1664,1667,1670,1673,1676,1679,1682,1685,1688,1691,1694,1697],{"className":1660},[689],[573,1662],{"className":1663},[689],[573,1665],{"className":1666,"style":718},[706],[573,1668,624],{"className":1669},[722],[573,1671],{"className":1672,"style":718},[706],[573,1674,1482],{"className":1675},[689],[573,1677],{"className":1678,"style":763},[706],[573,1680,817],{"className":1681},[767],[573,1683],{"className":1684,"style":763},[706],[573,1686,1400],{"className":1687},[689],[573,1689],{"className":1690,"style":763},[706],[573,1692,822],{"className":1693},[767],[573,1695],{"className":1696,"style":763},[706],[573,1698,1491],{"className":1699},[689],[573,1701,1702,1705],{"style":1604},[573,1703],{"className":1704,"style":1595},[1594],[573,1706,1708,1711,1714,1717,1720,1723,1726,1729,1732,1735,1738,1741,1744],{"className":1707},[689],[573,1709],{"className":1710},[689],[573,1712],{"className":1713,"style":718},[706],[573,1715,624],{"className":1716},[722],[573,1718],{"className":1719,"style":718},[706],[573,1721,1512],{"className":1722},[689],[573,1724],{"className":1725,"style":763},[706],[573,1727,817],{"className":1728},[767],[573,1730],{"className":1731,"style":763},[706],[573,1733,1491],{"className":1734},[689],[573,1736],{"className":1737,"style":763},[706],[573,1739,822],{"className":1740},[767],[573,1742],{"className":1743,"style":763},[706],[573,1745,1521],{"className":1746},[689],[573,1748,1749,1752],{"style":1616},[573,1750],{"className":1751,"style":1595},[1594],[573,1753,1755,1758,1761,1764,1767,1770,1773,1776,1779,1782,1785,1788,1791],{"className":1754},[689],[573,1756],{"className":1757},[689],[573,1759],{"className":1760,"style":718},[706],[573,1762,624],{"className":1763},[722],[573,1765],{"className":1766,"style":718},[706],[573,1768,1542],{"className":1769},[689],[573,1771],{"className":1772,"style":763},[706],[573,1774,817],{"className":1775},[767],[573,1777],{"className":1778,"style":763},[706],[573,1780,1521],{"className":1781},[689],[573,1783],{"className":1784,"style":763},[706],[573,1786,822],{"className":1787},[767],[573,1789],{"className":1790,"style":763},[706],[573,1792,916],{"className":1793},[689],[573,1795,1630],{"className":1796},[1629],[573,1798,1800],{"className":1799},[1582],[573,1801,1803],{"className":1802,"style":1637},[1586],[573,1804],{},[564,1806,1807,1808,1836,1837,1921],{},"Der letzte Rest ungleich null ist ",[573,1809,1811,1824],{"className":1810},[580],[573,1812,1814],{"className":1813},[584],[586,1815,1816],{"xmlns":588},[591,1817,1818,1822],{},[594,1819,1820],{},[914,1821,1521],{},[665,1823,1521],{"encoding":667},[573,1825,1827],{"className":1826,"ariaHidden":614},[672],[573,1828,1830,1833],{"className":1829},[676],[573,1831],{"className":1832,"style":1358},[680],[573,1834,1521],{"className":1835},[689],", also ",[573,1838,1840,1870],{"className":1839},[580],[573,1841,1843],{"className":1842},[584],[586,1844,1845],{"xmlns":588},[591,1846,1847,1867],{},[594,1848,1849,1851,1853,1855,1857,1859,1861,1863,1865],{},[597,1850,600],{"mathvariant":599},[602,1852,604],{},[602,1854,608],{"stretchy":607},[914,1856,1395],{},[602,1858,615],{"separator":614},[914,1860,1400],{},[602,1862,621],{"stretchy":607},[602,1864,624],{},[914,1866,1521],{},[665,1868,1869],{"encoding":667},"\\operatorname{ggT}(1071, 462) = 21",[573,1871,1873,1912],{"className":1872,"ariaHidden":614},[672],[573,1874,1876,1879,1885,1888,1891,1894,1897,1900,1903,1906,1909],{"className":1875},[676],[573,1877],{"className":1878,"style":681},[680],[573,1880,1882],{"className":1881},[685],[573,1883,600],{"className":1884},[689,690],[573,1886,608],{"className":1887},[694],[573,1889,1395],{"className":1890},[689],[573,1892,615],{"className":1893},[702],[573,1895],{"className":1896,"style":707},[706],[573,1898,1400],{"className":1899},[689],[573,1901,621],{"className":1902},[714],[573,1904],{"className":1905,"style":718},[706],[573,1907,624],{"className":1908},[722],[573,1910],{"className":1911,"style":718},[706],[573,1913,1915,1918],{"className":1914},[676],[573,1916],{"className":1917,"style":1358},[680],[573,1919,1521],{"className":1920},[689],".",[564,1923,1924,1439],{},[573,1925,1927,1955],{"className":1926},[580],[573,1928,1930],{"className":1929},[584],[586,1931,1932],{"xmlns":588},[591,1933,1934,1952],{},[594,1935,1936,1938,1940,1942,1945,1947,1950],{},[597,1937,600],{"mathvariant":599},[602,1939,604],{},[602,1941,608],{"stretchy":607},[914,1943,1944],{},"252",[602,1946,615],{"separator":614},[914,1948,1949],{},"105",[602,1951,621],{"stretchy":607},[665,1953,1954],{"encoding":667},"\\operatorname{ggT}(252, 105)",[573,1956,1958],{"className":1957,"ariaHidden":614},[672],[573,1959,1961,1964,1970,1973,1976,1979,1982,1985],{"className":1960},[676],[573,1962],{"className":1963,"style":681},[680],[573,1965,1967],{"className":1966},[685],[573,1968,600],{"className":1969},[689,690],[573,1971,608],{"className":1972},[694],[573,1974,1944],{"className":1975},[689],[573,1977,615],{"className":1978},[702],[573,1980],{"className":1981,"style":707},[706],[573,1983,1949],{"className":1984},[689],[573,1986,621],{"className":1987},[714],[573,1989,1991],{"className":1990},[576],[573,1992,1994,2091],{"className":1993},[580],[573,1995,1997],{"className":1996},[584],[586,1998,1999],{"xmlns":588,"display":589},[591,2000,2001,2088],{},[1454,2002,2003,2032,2060],{"rowspacing":1456,"columnalign":1457,"columnspacing":1458},[1460,2004,2005,2011],{},[1463,2006,2007],{},[1466,2008,2009],{"scriptlevel":916,"displaystyle":614},[914,2010,1944],{},[1463,2012,2013],{},[1466,2014,2015],{"scriptlevel":916,"displaystyle":614},[594,2016,2017,2019,2021,2023,2025,2027,2029],{},[594,2018],{},[602,2020,624],{},[914,2022,1482],{},[602,2024,817],{},[914,2026,1949],{},[602,2028,822],{},[914,2030,2031],{},"42",[1460,2033,2034,2040],{},[1463,2035,2036],{},[1466,2037,2038],{"scriptlevel":916,"displaystyle":614},[914,2039,1949],{},[1463,2041,2042],{},[1466,2043,2044],{"scriptlevel":916,"displaystyle":614},[594,2045,2046,2048,2050,2052,2054,2056,2058],{},[594,2047],{},[602,2049,624],{},[914,2051,1482],{},[602,2053,817],{},[914,2055,2031],{},[602,2057,822],{},[914,2059,1521],{},[1460,2061,2062,2068],{},[1463,2063,2064],{},[1466,2065,2066],{"scriptlevel":916,"displaystyle":614},[914,2067,2031],{},[1463,2069,2070],{},[1466,2071,2072],{"scriptlevel":916,"displaystyle":614},[594,2073,2074,2076,2078,2080,2082,2084,2086],{},[594,2075],{},[602,2077,624],{},[914,2079,1482],{},[602,2081,817],{},[914,2083,1521],{},[602,2085,822],{},[914,2087,916],{},[665,2089,2090],{"encoding":667},"\\begin{aligned}\n252 &= 2 \\cdot 105 + 42 \\\\\n105 &= 2 \\cdot 42 + 21 \\\\\n42 &= 2 \\cdot 21 + 0\n\\end{aligned}",[573,2092,2094],{"className":2093,"ariaHidden":614},[672],[573,2095,2097,2100],{"className":2096},[676],[573,2098],{"className":2099,"style":1563},[680],[573,2101,2103],{"className":2102},[689],[573,2104,2106,2162],{"className":2105},[1454],[573,2107,2109],{"className":2108},[1573],[573,2110,2112,2154],{"className":2111},[1577,1578],[573,2113,2115,2151],{"className":2114},[1582],[573,2116,2118,2129,2140],{"className":2117,"style":1587},[1586],[573,2119,2120,2123],{"style":1590},[573,2121],{"className":2122,"style":1595},[1594],[573,2124,2126],{"className":2125},[689],[573,2127,1944],{"className":2128},[689],[573,2130,2131,2134],{"style":1604},[573,2132],{"className":2133,"style":1595},[1594],[573,2135,2137],{"className":2136},[689],[573,2138,1949],{"className":2139},[689],[573,2141,2142,2145],{"style":1616},[573,2143],{"className":2144,"style":1595},[1594],[573,2146,2148],{"className":2147},[689],[573,2149,2031],{"className":2150},[689],[573,2152,1630],{"className":2153},[1629],[573,2155,2157],{"className":2156},[1582],[573,2158,2160],{"className":2159,"style":1637},[1586],[573,2161],{},[573,2163,2165],{"className":2164},[1643],[573,2166,2168,2318],{"className":2167},[1577,1578],[573,2169,2171,2315],{"className":2170},[1582],[573,2172,2174,2221,2268],{"className":2173,"style":1587},[1586],[573,2175,2176,2179],{"style":1590},[573,2177],{"className":2178,"style":1595},[1594],[573,2180,2182,2185,2188,2191,2194,2197,2200,2203,2206,2209,2212,2215,2218],{"className":2181},[689],[573,2183],{"className":2184},[689],[573,2186],{"className":2187,"style":718},[706],[573,2189,624],{"className":2190},[722],[573,2192],{"className":2193,"style":718},[706],[573,2195,1482],{"className":2196},[689],[573,2198],{"className":2199,"style":763},[706],[573,2201,817],{"className":2202},[767],[573,2204],{"className":2205,"style":763},[706],[573,2207,1949],{"className":2208},[689],[573,2210],{"className":2211,"style":763},[706],[573,2213,822],{"className":2214},[767],[573,2216],{"className":2217,"style":763},[706],[573,2219,2031],{"className":2220},[689],[573,2222,2223,2226],{"style":1604},[573,2224],{"className":2225,"style":1595},[1594],[573,2227,2229,2232,2235,2238,2241,2244,2247,2250,2253,2256,2259,2262,2265],{"className":2228},[689],[573,2230],{"className":2231},[689],[573,2233],{"className":2234,"style":718},[706],[573,2236,624],{"className":2237},[722],[573,2239],{"className":2240,"style":718},[706],[573,2242,1482],{"className":2243},[689],[573,2245],{"className":2246,"style":763},[706],[573,2248,817],{"className":2249},[767],[573,2251],{"className":2252,"style":763},[706],[573,2254,2031],{"className":2255},[689],[573,2257],{"className":2258,"style":763},[706],[573,2260,822],{"className":2261},[767],[573,2263],{"className":2264,"style":763},[706],[573,2266,1521],{"className":2267},[689],[573,2269,2270,2273],{"style":1616},[573,2271],{"className":2272,"style":1595},[1594],[573,2274,2276,2279,2282,2285,2288,2291,2294,2297,2300,2303,2306,2309,2312],{"className":2275},[689],[573,2277],{"className":2278},[689],[573,2280],{"className":2281,"style":718},[706],[573,2283,624],{"className":2284},[722],[573,2286],{"className":2287,"style":718},[706],[573,2289,1482],{"className":2290},[689],[573,2292],{"className":2293,"style":763},[706],[573,2295,817],{"className":2296},[767],[573,2298],{"className":2299,"style":763},[706],[573,2301,1521],{"className":2302},[689],[573,2304],{"className":2305,"style":763},[706],[573,2307,822],{"className":2308},[767],[573,2310],{"className":2311,"style":763},[706],[573,2313,916],{"className":2314},[689],[573,2316,1630],{"className":2317},[1629],[573,2319,2321],{"className":2320},[1582],[573,2322,2324],{"className":2323,"style":1637},[1586],[573,2325],{},[564,2327,2328,2329,1921],{},"Ergebnis: ",[573,2330,2332,2362],{"className":2331},[580],[573,2333,2335],{"className":2334},[584],[586,2336,2337],{"xmlns":588},[591,2338,2339,2359],{},[594,2340,2341,2343,2345,2347,2349,2351,2353,2355,2357],{},[597,2342,600],{"mathvariant":599},[602,2344,604],{},[602,2346,608],{"stretchy":607},[914,2348,1944],{},[602,2350,615],{"separator":614},[914,2352,1949],{},[602,2354,621],{"stretchy":607},[602,2356,624],{},[914,2358,1521],{},[665,2360,2361],{"encoding":667},"\\operatorname{ggT}(252, 105) = 21",[573,2363,2365,2404],{"className":2364,"ariaHidden":614},[672],[573,2366,2368,2371,2377,2380,2383,2386,2389,2392,2395,2398,2401],{"className":2367},[676],[573,2369],{"className":2370,"style":681},[680],[573,2372,2374],{"className":2373},[685],[573,2375,600],{"className":2376},[689,690],[573,2378,608],{"className":2379},[694],[573,2381,1944],{"className":2382},[689],[573,2384,615],{"className":2385},[702],[573,2387],{"className":2388,"style":707},[706],[573,2390,1949],{"className":2391},[689],[573,2393,621],{"className":2394},[714],[573,2396],{"className":2397,"style":718},[706],[573,2399,624],{"className":2400},[722],[573,2402],{"className":2403,"style":718},[706],[573,2405,2407,2410],{"className":2406},[676],[573,2408],{"className":2409,"style":1358},[680],[573,2411,1521],{"className":2412},[689],[559,2414,2416],{"id":2415},"typische-fehler","Typische Fehler",[2418,2419,2420,2546,2552,2681],"ul",{},[2421,2422,2423,2455,2456,2459,2460,2488,2489,2517,2518,1921],"li",{},[568,2424,2425,2426,2454],{},"Den Rest ",[573,2427,2429,2442],{"className":2428},[580],[573,2430,2432],{"className":2431},[584],[586,2433,2434],{"xmlns":588},[591,2435,2436,2440],{},[594,2437,2438],{},[914,2439,916],{},[665,2441,916],{"encoding":667},[573,2443,2445],{"className":2444,"ariaHidden":614},[672],[573,2446,2448,2451],{"className":2447},[676],[573,2449],{"className":2450,"style":1358},[680],[573,2452,916],{"className":2453},[689]," oder den letzten Quotienten als Ergebnis nehmen."," Der ggT ist der letzte Rest ",[568,2457,2458],{},"vor"," der ",[573,2461,2463,2476],{"className":2462},[580],[573,2464,2466],{"className":2465},[584],[586,2467,2468],{"xmlns":588},[591,2469,2470,2474],{},[594,2471,2472],{},[914,2473,916],{},[665,2475,916],{"encoding":667},[573,2477,2479],{"className":2478,"ariaHidden":614},[672],[573,2480,2482,2485],{"className":2481},[676],[573,2483],{"className":2484,"style":1358},[680],[573,2486,916],{"className":2487},[689],", im ersten Beispiel ",[573,2490,2492,2505],{"className":2491},[580],[573,2493,2495],{"className":2494},[584],[586,2496,2497],{"xmlns":588},[591,2498,2499,2503],{},[594,2500,2501],{},[914,2502,1521],{},[665,2504,1521],{"encoding":667},[573,2506,2508],{"className":2507,"ariaHidden":614},[672],[573,2509,2511,2514],{"className":2510},[676],[573,2512],{"className":2513,"style":1358},[680],[573,2515,1521],{"className":2516},[689],", nicht der Quotient ",[573,2519,2521,2534],{"className":2520},[580],[573,2522,2524],{"className":2523},[584],[586,2525,2526],{"xmlns":588},[591,2527,2528,2532],{},[594,2529,2530],{},[914,2531,1542],{},[665,2533,1542],{"encoding":667},[573,2535,2537],{"className":2536,"ariaHidden":614},[672],[573,2538,2540,2543],{"className":2539},[676],[573,2541],{"className":2542,"style":1358},[680],[573,2544,1542],{"className":2545},[689],[2421,2547,2548,2551],{},[568,2549,2550],{},"Quotient und Rest verwechseln."," Weiter geht es immer mit dem Paar (alter Divisor, Rest), nicht mit dem Quotienten.",[2421,2553,2554,2557,2558,2621,2622,2650,2651,2680],{},[568,2555,2556],{},"Nach dem ersten Schritt aufhören."," Bei ",[573,2559,2561,2588],{"className":2560},[580],[573,2562,2564],{"className":2563},[584],[586,2565,2566],{"xmlns":588},[591,2567,2568,2585],{},[594,2569,2570,2572,2574,2576,2579,2581,2583],{},[597,2571,600],{"mathvariant":599},[602,2573,604],{},[602,2575,608],{"stretchy":607},[914,2577,2578],{},"34",[602,2580,615],{"separator":614},[914,2582,1521],{},[602,2584,621],{"stretchy":607},[665,2586,2587],{"encoding":667},"\\operatorname{ggT}(34, 21)",[573,2589,2591],{"className":2590,"ariaHidden":614},[672],[573,2592,2594,2597,2603,2606,2609,2612,2615,2618],{"className":2593},[676],[573,2595],{"className":2596,"style":681},[680],[573,2598,2600],{"className":2599},[685],[573,2601,600],{"className":2602},[689,690],[573,2604,608],{"className":2605},[694],[573,2607,2578],{"className":2608},[689],[573,2610,615],{"className":2611},[702],[573,2613],{"className":2614,"style":707},[706],[573,2616,1521],{"className":2617},[689],[573,2619,621],{"className":2620},[714]," braucht man sieben Divisionen, bis der Rest ",[573,2623,2625,2638],{"className":2624},[580],[573,2626,2628],{"className":2627},[584],[586,2629,2630],{"xmlns":588},[591,2631,2632,2636],{},[594,2633,2634],{},[914,2635,916],{},[665,2637,916],{"encoding":667},[573,2639,2641],{"className":2640,"ariaHidden":614},[672],[573,2642,2644,2647],{"className":2643},[676],[573,2645],{"className":2646,"style":1358},[680],[573,2648,916],{"className":2649},[689]," ist; das Ergebnis ist ",[573,2652,2654,2668],{"className":2653},[580],[573,2655,2657],{"className":2656},[584],[586,2658,2659],{"xmlns":588},[591,2660,2661,2666],{},[594,2662,2663],{},[914,2664,2665],{},"1",[665,2667,2665],{"encoding":667},[573,2669,2671],{"className":2670,"ariaHidden":614},[672],[573,2672,2674,2677],{"className":2673},[676],[573,2675],{"className":2676,"style":1358},[680],[573,2678,2665],{"className":2679},[689],", die Zahlen sind teilerfremd.",[2421,2682,2683,2738,2739,2789,2790,1921],{},[568,2684,2685,2686,2737],{},"Mit ",[573,2687,2689,2707],{"className":2688},[580],[573,2690,2692],{"className":2691},[584],[586,2693,2694],{"xmlns":588},[591,2695,2696,2704],{},[594,2697,2698,2700,2702],{},[597,2699,618],{},[602,2701,624],{},[914,2703,916],{},[665,2705,2706],{"encoding":667},"b = 0",[573,2708,2710,2728],{"className":2709,"ariaHidden":614},[672],[573,2711,2713,2716,2719,2722,2725],{"className":2712},[676],[573,2714],{"className":2715,"style":977},[680],[573,2717,618],{"className":2718},[689,698],[573,2720],{"className":2721,"style":718},[706],[573,2723,624],{"className":2724},[722],[573,2726],{"className":2727,"style":718},[706],[573,2729,2731,2734],{"className":2730},[676],[573,2732],{"className":2733,"style":1358},[680],[573,2735,916],{"className":2736},[689]," teilen wollen."," Für ",[573,2740,2742,2759],{"className":2741},[580],[573,2743,2745],{"className":2744},[584],[586,2746,2747],{"xmlns":588},[591,2748,2749,2757],{},[594,2750,2751,2753,2755],{},[597,2752,618],{},[602,2754,624],{},[914,2756,916],{},[665,2758,2706],{"encoding":667},[573,2760,2762,2780],{"className":2761,"ariaHidden":614},[672],[573,2763,2765,2768,2771,2774,2777],{"className":2764},[676],[573,2766],{"className":2767,"style":977},[680],[573,2769,618],{"className":2770},[689,698],[573,2772],{"className":2773,"style":718},[706],[573,2775,624],{"className":2776},[722],[573,2778],{"className":2779,"style":718},[706],[573,2781,2783,2786],{"className":2782},[676],[573,2784],{"className":2785,"style":1358},[680],[573,2787,916],{"className":2788},[689]," gilt direkt ",[573,2791,2793,2823],{"className":2792},[580],[573,2794,2796],{"className":2795},[584],[586,2797,2798],{"xmlns":588},[591,2799,2800,2820],{},[594,2801,2802,2804,2806,2808,2810,2812,2814,2816,2818],{},[597,2803,600],{"mathvariant":599},[602,2805,604],{},[602,2807,608],{"stretchy":607},[597,2809,611],{},[602,2811,615],{"separator":614},[914,2813,916],{},[602,2815,621],{"stretchy":607},[602,2817,624],{},[597,2819,611],{},[665,2821,2822],{"encoding":667},"\\operatorname{ggT}(a, 0) = a",[573,2824,2826,2865],{"className":2825,"ariaHidden":614},[672],[573,2827,2829,2832,2838,2841,2844,2847,2850,2853,2856,2859,2862],{"className":2828},[676],[573,2830],{"className":2831,"style":681},[680],[573,2833,2835],{"className":2834},[685],[573,2836,600],{"className":2837},[689,690],[573,2839,608],{"className":2840},[694],[573,2842,611],{"className":2843},[689,698],[573,2845,615],{"className":2846},[702],[573,2848],{"className":2849,"style":707},[706],[573,2851,916],{"className":2852},[689],[573,2854,621],{"className":2855},[714],[573,2857],{"className":2858,"style":718},[706],[573,2860,624],{"className":2861},[722],[573,2863],{"className":2864,"style":718},[706],[573,2866,2868,2871],{"className":2867},[676],[573,2869],{"className":2870,"style":838},[680],[573,2872,611],{"className":2873},[689,698],{"title":2875,"searchDepth":2876,"depth":2876,"links":2877},"",2,[2878,2879,2880],{"id":561,"depth":2876,"text":562},{"id":1371,"depth":2876,"text":1372},{"id":2415,"depth":2876,"text":2416},[2882,2888,2892,2894,2896,2898,2900,2902,2904,2906,2908],{"lhs":2883,"rhs":2884,"where":2885},"gcd(a, b)","gcd(b, mod(a, b))",{"a":2886,"b":2887},1071,462,{"lhs":2883,"rhs":2884,"where":2889},{"a":2890,"b":2891},252,105,{"lhs":2893,"rhs":1395},"2*462 + 147",{"lhs":2895,"rhs":1400},"3*147 + 21",{"lhs":2897,"rhs":1491},"7*21",{"lhs":2899,"rhs":1521},"gcd(1071, 462)",{"lhs":2901,"rhs":1944},"2*105 + 42",{"lhs":2903,"rhs":1949},"2*42 + 21",{"lhs":2905,"rhs":2031},"2*21",{"lhs":2907,"rhs":1521},"gcd(252, 105)",{"lhs":2909,"rhs":2665},"gcd(34, 21)","a, b \\in \\mathbb{N}_0;\\ b \\geq 1 \\text{ in der ersten, } a \\geq 1 \\text{ in der zweiten Gleichung}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\in \\mathbb{N}_0;\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 mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\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\">\u003Cspan class=\"mord mathbb\">N\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\">0\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>\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>b\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\geq 1\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:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\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\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">in der ersten,\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\geq 1\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\">a\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\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">in der zweiten Gleichung\u003C\u002Fspan>",null,"md","euclidean-algorithm","\\operatorname{ggT}(a, b) = \\operatorname{ggT}(b,\\ a \\bmod b), \\qquad \\operatorname{ggT}(a, 0) = a","\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 mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>a\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo lspace=\"0.22em\" rspace=\"0.22em\">\u003Cmrow>\u003Cmi mathvariant=\"normal\">m\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">o\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">d\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{ggT}(a, b) = \\operatorname{ggT}(b,\\ a \\bmod b), \\qquad \\operatorname{ggT}(a, 0) = a\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=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.0556em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathrm\">mod\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.0556em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Feuklidischer-algorithmus",[],[2923,2924,2925],"extended-euclidean","gcd-lcm","prime-factorization",{"title":548,"description":2875},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Feuklidischer-algorithmus","Der ggT zweier Zahlen ändert sich nicht, wenn man die größere durch ihren Rest bei Division durch die kleinere ersetzt.",[2930,2931,2932,2933],"ggt","division mit rest","zahlentheorie","algorithmus",[2935,2939,2943],{"symbol":2936,"meaning":2937,"symbolHtml":2938},"a, b","natürliche Zahlen, deren größter gemeinsamer Teiler gesucht ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\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 mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2940,"meaning":2941,"symbolHtml":2942},"\\operatorname{ggT}(a, b)","größter gemeinsamer Teiler von a und b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">ggT\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{ggT}(a, b)\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=\"mop\">\u003Cspan class=\"mord mathrm\">ggT\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2944,"meaning":2945,"symbolHtml":2946},"a \\bmod b","Rest bei der Division von a durch b, eine Zahl zwischen 0 und b−1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo lspace=\"0.22em\" rspace=\"0.22em\">\u003Cmrow>\u003Cmi mathvariant=\"normal\">m\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">o\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">d\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\bmod b\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.0556em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathrm\">mod\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.0556em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","P6Ec-mAi44YPAbmogHAeyy8p8JUspazg-Ikdttaiykg",[2949,2952,2955],{"stem":2950,"title":2951,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv","Zusammenhang von ggT und kgV",{"stem":2953,"title":2954,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung","Primfaktorzerlegung",{"stem":2956,"title":2957,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Ferweiterter-euklidischer-algorithmus","Erweiterter Euklidischer Algorithmus",1793824276036]