今回は2021の階乗と計算を紹介していきます。
2021の階乗は780301939641810967074983593480004010572394377037320870339932574723966706382721791411178029344753942260021646442166449239309305420699740533529828443589112978094315790589459115326726585869546644590908033098153851723150840546431060437829309929122989052138893293095717989024686169296836492987257898785910446072885809293171865573703296237512433567336672022631132172394927379718554144858216145432627533050575069768224634069083225560131319408356707719577100877446756253521099166294151331063052114155348082382141193544871388964283464166203625622856263467554508022686652096106294985733166343382741204598232191740006115120381344621454099472751707285028158339089563264977347451074041037901095306333709664013882162181080383039590828706818236222981658901457062152647445154000936996828867567690980674705602666907472420819186380161990644490680163494011932695362610443267340063442335950257278429174928688195087730349385939000051936359615055118740957370895242822871810042873611830306487128768314103158506722934736540499576237686159292393026624492152037090070050539804315405257794060763160546185072752891849878247143547035570917842651029768123535065040189220693063724220427998564446050129399450528231961867671902073503714638709802999886156065797348018055886010130170092306234514701066474486505376581014591917552236939747078183734714955219454819248088300532846165921286474769220204343058064998727463603556812435163614730855653311130219426570655986015161129200010293054908937885833367227611315439661603796735752083679191774122219453503676117273445314723805749338096711271742982110976161478181150421397227730317993564200527238655136517406365400691604284604845773791330376289049391859575615875632242440709751589145133131309102380068232347730966920165747724814559874418267019839453934327816515478621068155536550177747346895232562582240719823576655603572048984460998051952229007006356892481491678624694893810650123790495440640134003510087871692760032258497489479480424882647313017302347991777928826854362195970065209888944374390761513846257451454835378743173779575914582777988931069508064658567342309756802353615450586127512329778124058943102597576667700134121814593178926679202027401760597799753163451313769855457973533464474520488908106155686324944119641987148333739639693359029358483191617555335658740439390537837278371270000828135036374429298801437068859524805420017293270427190621305805491275820869133751761919421093801688054215928961450417135105154956607070365359382071399563720716902512665655073536026606391572535966437831137575236900215197411591997207736594539288867882045142782375101143304407056515153034989676364678650107291257453336110600680913939743545979168475042779626770487989463924458778901252823396153394107247545572609993304026911021649171014825344115589047362712623811767324263454051274259839024046567028438332960950964921155349991528264004041045982369924412730462297441658699116815129948096261922043029535054640935595413022601779162325260035004065234579963430351868988154580511616634792816261344935960501810827951677958955449116747383654178065615836265530720711161023200382466653010015956567555565606194735777205681435712326998368638864797275563569418099390932810895164937566755717188171660992599991698138419962564397505551034202344637476584684811834277777111564369332918135325784416461504336121064154696962239781363873994154778140588176184111189337325080180262015940773870152747304915934188425061582840648455526307416093282414335371926832791745977085626772473956222980200680785163253108024668583345104356741158057995812126065862186744805980816925775209978305537055294644656634866722865068470317764807615449439524541974645516864308432896984747772268655579175939996960229445274177091712036424158720771740448711517943606650158493342016651189756518333818511037998572951066985967202267039200351180918488073398670524394117437744810885007795507177047177545965632474884268091962501711580693757649334928909590537345820588458253268832282514752893102626261248658470743161469247797099494483980065008796825854748617293499435491478646556482366125281042409677847432503669757158827485751628682798093718383304737294319990899513459327366794697585146593327770589640781801056779352414447791909011385603543648156524690528843689847364360206117363709357562940498728411553026177458020628240096631232055936679876118807606548242842884120011585990723525218511873660381242388270117325422241615210134418992334221904134185064882718412291242381047136274775082253474935319163866239922009296246556803564738354387983614081402912654940111073825061735872837675609134590073443995233461425487886267715992957978621586302713968268195387966922871231631216384190629025939069760463690935736733630754730098009880850259269340707709072565248071993580643836303357409034046212220139244434602402886343470527833076513180890817531028951238075086312396228533818119617879660769767003663161539394965337969406515535017836410560131301353749293160452161327983366834547819591084007070485774558921027334241610500167367452620112858675752740829304685725252296875999468026869421370304612439392098608873767179010707198609701108953513945478402058908829389316905283851885487141835285828517101033402635916116042881865710677928980487585322968883667989112048427476801546515659682983814274581092453457932967134906646473266909828157068480286394819951845111027426080498856755200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000で表すと。
この計算方法について紹介していきます。
階乗とは何か？
まず、階乗とは何かを理解することが大切です。
階乗は、ある自然数nに対して、1からnまでの全ての数を掛け合わせたものです。
つまり、nの階乗は、$n!=n(n-1)(n-2)…3\times2\times1$です。
※参考記事
[数A]階乗｜階乗とは、0の階乗が1になる理由も解説
2021の階乗
ここから、本題に入りましょう。
nの階乗の式に2021を代入して計算します。
$$n!=n(n-1)(n-2)…3\times2\times1$$
ここで$n=2021$とすると、下記のように計算できます。
$$2021!=2021\times2020\times2019\times2018\times2017\times2016\times2015\times2014\times2013\times2012\times2011\times2010\times2009\times2008\times2007\times2006\times2005\times2004\times2003\times2002\times2001\times2000\times1999\times1998\times1997\times1996\times1995\times1994\times1993\times1992\times1991\times1990\times1989\times1988\times1987\times1986\times1985\times1984\times1983\times1982\times1981\times1980\times1979\times1978\times1977\times1976\times1975\times1974\times1973\times1972\times1971\times1970\times1969\times1968\times1967\times1966\times1965\times1964\times1963\times1962\times1961\times1960\times1959\times1958\times1957\times1956\times1955\times1954\times1953\times1952\times1951\times1950\times1949\times1948\times1947\times1946\times1945\times1944\times1943\times1942\times1941\times1940\times1939\times1938\times1937\times1936\times1935\times1934\times1933\times1932\times1931\times1930\times1929\times1928\times1927\times1926\times1925\times1924\times1923\times1922\times1921\times1920\times1919\times1918\times1917\times1916\times1915\times1914\times1913\times1912\times1911\times1910\times1909\times1908\times1907\times1906\times1905\times1904\times1903\times1902\times1901\times1900\times1899\times1898\times1897\times1896\times1895\times1894\times1893\times1892\times1891\times1890\times1889\times1888\times1887\times1886\times1885\times1884\times1883\times1882\times1881\times1880\times1879\times1878\times1877\times1876\times1875\times1874\times1873\times1872\times1871\times1870\times1869\times1868\times1867\times1866\times1865\times1864\times1863\times1862\times1861\times1860\times1859\times1858\times1857\times1856\times1855\times1854\times1853\times1852\times1851\times1850\times1849\times1848\times1847\times1846\times1845\times1844\times1843\times1842\times1841\times1840\times1839\times1838\times1837\times1836\times1835\times1834\times1833\times1832\times1831\times1830\times1829\times1828\times1827\times1826\times1825\times1824\times1823\times1822\times1821\times1820\times1819\times1818\times1817\times1816\times1815\times1814\times1813\times1812\times1811\times1810\times1809\times1808\times1807\times1806\times1805\times1804\times1803\times1802\times1801\times1800\times1799\times1798\times1797\times1796\times1795\times1794\times1793\times1792\times1791\times1790\times1789\times1788\times1787\times1786\times1785\times1784\times1783\times1782\times1781\times1780\times1779\times1778\times1777\times1776\times1775\times1774\times1773\times1772\times1771\times1770\times1769\times1768\times1767\times1766\times1765\times1764\times1763\times1762\times1761\times1760\times1759\times1758\times1757\times1756\times1755\times1754\times1753\times1752\times1751\times1750\times1749\times1748\times1747\times1746\times1745\times1744\times1743\times1742\times1741\times1740\times1739\times1738\times1737\times1736\times1735\times1734\times1733\times1732\times1731\times1730\times1729\times1728\times1727\times1726\times1725\times1724\times1723\times1722\times1721\times1720\times1719\times1718\times1717\times1716\times1715\times1714\times1713\times1712\times1711\times1710\times1709\times1708\times1707\times1706\times1705\times1704\times1703\times1702\times1701\times1700\times1699\times1698\times1697\times1696\times1695\times1694\times1693\times1692\times1691\times1690\times1689\times1688\times1687\times1686\times1685\times1684\times1683\times1682\times1681\times1680\times1679\times1678\times1677\times1676\times1675\times1674\times1673\times1672\times1671\times1670\times1669\times1668\times1667\times1666\times1665\times1664\times1663\times1662\times1661\times1660\times1659\times1658\times1657\times1656\times1655\times1654\times1653\times1652\times1651\times1650\times1649\times1648\times1647\times1646\times1645\times1644\times1643\times1642\times1641\times1640\times1639\times1638\times1637\times1636\times1635\times1634\times1633\times1632\times1631\times1630\times1629\times1628\times1627\times1626\times1625\times1624\times1623\times1622\times1621\times1620\times1619\times1618\times1617\times1616\times1615\times1614\times1613\times1612\times1611\times1610\times1609\times1608\times1607\times1606\times1605\times1604\times1603\times1602\times1601\times1600\times1599\times1598\times1597\times1596\times1595\times1594\times1593\times1592\times1591\times1590\times1589\times1588\times1587\times1586\times1585\times1584\times1583\times1582\times1581\times1580\times1579\times1578\times1577\times1576\times1575\times1574\times1573\times1572\times1571\times1570\times1569\times1568\times1567\times1566\times1565\times1564\times1563\times1562\times1561\times1560\times1559\times1558\times1557\times1556\times1555\times1554\times1553\times1552\times1551\times1550\times1549\times1548\times1547\times1546\times1545\times1544\times1543\times1542\times1541\times1540\times1539\times1538\times1537\times1536\times1535\times1534\times1533\times1532\times1531\times1530\times1529\times1528\times1527\times1526\times1525\times1524\times1523\times15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掛け算だけで求められるので計算は難しくないですね。
nの値が大きい時は迷わず電卓やエクセルを使いましょう！
まとめ
ここまで読んでいただきありがとうございます。
2021の階乗を計算してきました。
nの階乗は、$n!=n(n-1)(n-2)…3\times2\times1$なので、nに代入すれば掛け算だけでも解けますね！
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