阶乘值表
阶乘 n! = 1 × 2 × … × n，是从 1 乘到 n 的全部整数之积，也是排列组合公式的基本积木。 本表覆盖 0! 到 100! 全部 101 个精确值：从 0! = 1 到 100! 的 158 位大数（末尾 24 个零）， 每个值附素因数分解、末尾零计数与递推链，点击任意值进入详解页。
十个经典阶乘
0!
1
5!
120
10!
3,628,800
18!
6,402,373,705,728,000
20!
2,432,902,008,176,640,000
21!
51,090,942,171,709,440,000
52!
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
69!
171,122,452,428,141,311,372,468,338,881,272,839,092,270,544,893,520,369,393,648,040,923,257,279,754,140,647,424,000,000,000,000,000
70!
11,978,571,669,969,891,796,072,783,721,689,098,736,458,938,142,546,425,857,555,362,864,628,009,582,789,845,319,680,000,000,000,000,000
100!
93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000
规律一：递推与边界
n! = n × (n-1)!，每项只需一次乘法：1! = 1 × 0! = 1，2! = 2，3! = 6…… 但边界来得很快：18! 是双精度浮点能精确表示的最后一个阶乘，21! 超出 64 位无符号整数， 171! 超出双精度可表示范围——本表 BigInt 递推保证 100! 末位分毫不差。
规律二：末尾零与素因数
末尾零由因子 5 决定（2 远多于 5）：100! 末尾 ⌊100/5⌋ + ⌊100/25⌋ = 24 个零。 每个素数 p 在 n! 中出现 Σ⌊n/p^i⌋ 次——97 在 100! 中只出现 1 次，2 出现 97 次。 Stirling 公式 n! ≈ (n/e)^n √(2πn) 给出增长速度：超指数，比任何固定底的幂都快。
全量阶乘值（按区间分组）
10! - 24!
10! = 3628800 破七位数；18! 是 Number 精确上限、20!/21! 跨过 uint64 边界。
10!3,628,80011!39,916,80012!479,001,60013!6,227,020,80014!87,178,291,20015!1,307,674,368,00016!20,922,789,888,00017!355,687,428,096,00018!6,402,373,705,728,00019!121,645,100,408,832,00020!2,432,902,008,176,640,00021!51,090,942,171,709,440,00022!1,124,000,727,777,607,680,00023!25,852,016,738,884,976,640,00024!620,448,401,733,239,439,360,000
25! - 49!
25! ≈ 1.55 × 10^25 到 49! ≈ 6.1 × 10^62；末尾零快速堆积。
25!15,511,210,043,330,985,984,000,00026!403,291,461,126,605,635,584,000,00027!10,888,869,450,418,352,160,768,000,00028!304,888,344,611,713,860,501,504,000,00029!8,841,761,993,739,701,954,543,616,000,00030!265,252,859,812,191,058,636,308,480,000,00031!8,222,838,654,177,922,817,725,562,880,000,00032!263,130,836,933,693,530,167,218,012,160,000,00033!8,683,317,618,811,886,495,518,194,401,280,000,00034!295,232,799,039,604,140,847,618,609,643,520,000,00035!10,333,147,966,386,144,929,666,651,337,523,200,000,00036!371,993,326,789,901,217,467,999,448,150,835,200,000,00037!13,763,753,091,226,345,046,315,979,581,580,902,400,000,00038!523,022,617,466,601,111,760,007,224,100,074,291,200,000,00039!20,397,882,081,197,443,358,640,281,739,902,897,356,800,000,00040!815,915,283,247,897,734,345,611,269,596,115,894,272,000,000,00041!33,452,526,613,163,807,108,170,062,053,440,751,665,152,000,000,00042!1,405,006,117,752,879,898,543,142,606,244,511,569,936,384,000,000,00043!60,415,263,063,373,835,637,355,132,068,513,997,507,264,512,000,000,00044!2,658,271,574,788,448,768,043,625,811,014,615,890,319,638,528,000,000,00045!119,622,220,865,480,194,561,963,161,495,657,715,064,383,733,760,000,000,00046!5,502,622,159,812,088,949,850,305,428,800,254,892,961,651,752,960,000,000,00047!258,623,241,511,168,180,642,964,355,153,611,979,969,197,632,389,120,000,000,00048!12,413,915,592,536,072,670,862,289,047,373,375,038,521,486,354,677,760,000,000,00049!608,281,864,034,267,560,872,252,163,321,295,376,887,552,831,379,210,240,000,000,000
50! - 74!
52! 一副扑克的洗牌宇宙；70! ≈ 1.19 × 10^100 首次超越 Googol。
50!30,414,093,201,713,378,043,612,608,166,064,768,844,377,641,568,960,512,000,000,000,00051!1,551,118,753,287,382,280,224,243,016,469,303,211,063,259,720,016,986,112,000,000,000,00052!80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,00053!4,274,883,284,060,025,564,298,013,753,389,399,649,690,343,788,366,813,724,672,000,000,000,00054!230,843,697,339,241,380,472,092,742,683,027,581,083,278,564,571,807,941,132,288,000,000,000,00055!12,696,403,353,658,275,925,965,100,847,566,516,959,580,321,051,449,436,762,275,840,000,000,000,00056!710,998,587,804,863,451,854,045,647,463,724,949,736,497,978,881,168,458,687,447,040,000,000,000,00057!40,526,919,504,877,216,755,680,601,905,432,322,134,980,384,796,226,602,145,184,481,280,000,000,000,00058!2,350,561,331,282,878,571,829,474,910,515,074,683,828,862,318,181,142,924,420,699,914,240,000,000,000,00059!138,683,118,545,689,835,737,939,019,720,389,406,345,902,876,772,687,432,540,821,294,940,160,000,000,000,00060!8,320,987,112,741,390,144,276,341,183,223,364,380,754,172,606,361,245,952,449,277,696,409,600,000,000,000,00061!507,580,213,877,224,798,800,856,812,176,625,227,226,004,528,988,036,003,099,405,939,480,985,600,000,000,000,00062!31,469,973,260,387,937,525,653,122,354,950,764,088,012,280,797,258,232,192,163,168,247,821,107,200,000,000,000,00063!1,982,608,315,404,440,064,116,146,708,361,898,137,544,773,690,227,268,628,106,279,599,612,729,753,600,000,000,000,00064!126,886,932,185,884,164,103,433,389,335,161,480,802,865,516,174,545,192,198,801,894,375,214,704,230,400,000,000,000,00065!8,247,650,592,082,470,666,723,170,306,785,496,252,186,258,551,345,437,492,922,123,134,388,955,774,976,000,000,000,000,00066!544,344,939,077,443,064,003,729,240,247,842,752,644,293,064,388,798,874,532,860,126,869,671,081,148,416,000,000,000,000,00067!36,471,110,918,188,685,288,249,859,096,605,464,427,167,635,314,049,524,593,701,628,500,267,962,436,943,872,000,000,000,000,00068!2,480,035,542,436,830,599,600,990,418,569,171,581,047,399,201,355,367,672,371,710,738,018,221,445,712,183,296,000,000,000,000,00069!171,122,452,428,141,311,372,468,338,881,272,839,092,270,544,893,520,369,393,648,040,923,257,279,754,140,647,424,000,000,000,000,00070!11,978,571,669,969,891,796,072,783,721,689,098,736,458,938,142,546,425,857,555,362,864,628,009,582,789,845,319,680,000,000,000,000,00071!850,478,588,567,862,317,521,167,644,239,926,010,288,584,608,120,796,235,886,430,763,388,588,680,378,079,017,697,280,000,000,000,000,00072!61,234,458,376,886,086,861,524,070,385,274,672,740,778,091,784,697,328,983,823,014,963,978,384,987,221,689,274,204,160,000,000,000,000,00073!4,470,115,461,512,684,340,891,257,138,125,051,110,076,800,700,282,905,015,819,080,092,370,422,104,067,183,317,016,903,680,000,000,000,000,00074!330,788,544,151,938,641,225,953,028,221,253,782,145,683,251,820,934,971,170,611,926,835,411,235,700,971,565,459,250,872,320,000,000,000,000,000
75! - 100!
大数区间：100! = 9.33 × 10^157（158 位，末尾 24 个零）收官。
75!24,809,140,811,395,398,091,946,477,116,594,033,660,926,243,886,570,122,837,795,894,512,655,842,677,572,867,409,443,815,424,000,000,000,000,000,00076!1,885,494,701,666,050,254,987,932,260,861,146,558,230,394,535,379,329,335,672,487,982,961,844,043,495,537,923,117,729,972,224,000,000,000,000,000,00077!145,183,092,028,285,869,634,070,784,086,308,284,983,740,379,224,208,358,846,781,574,688,061,991,349,156,420,080,065,207,861,248,000,000,000,000,000,00078!11,324,281,178,206,297,831,457,521,158,732,046,228,731,749,579,488,251,990,048,962,825,668,835,325,234,200,766,245,086,213,177,344,000,000,000,000,000,00079!894,618,213,078,297,528,685,144,171,539,831,652,069,808,216,779,571,907,213,868,063,227,837,990,693,501,860,533,361,810,841,010,176,000,000,000,000,000,00080!71,569,457,046,263,802,294,811,533,723,186,532,165,584,657,342,365,752,577,109,445,058,227,039,255,480,148,842,668,944,867,280,814,080,000,000,000,000,000,00081!5,797,126,020,747,367,985,879,734,231,578,109,105,412,357,244,731,625,958,745,865,049,716,390,179,693,892,056,256,184,534,249,745,940,480,000,000,000,000,000,00082!475,364,333,701,284,174,842,138,206,989,404,946,643,813,294,067,993,328,617,160,934,076,743,994,734,899,148,613,007,131,808,479,167,119,360,000,000,000,000,000,00083!39,455,239,697,206,586,511,897,471,180,120,610,571,436,503,407,643,446,275,224,357,528,369,751,562,996,629,334,879,591,940,103,770,870,906,880,000,000,000,000,000,00084!3,314,240,134,565,353,266,999,387,579,130,131,288,000,666,286,242,049,487,118,846,032,383,059,131,291,716,864,129,885,722,968,716,753,156,177,920,000,000,000,000,000,00085!281,710,411,438,055,027,694,947,944,226,061,159,480,056,634,330,574,206,405,101,912,752,560,026,159,795,933,451,040,286,452,340,924,018,275,123,200,000,000,000,000,000,00086!24,227,095,383,672,732,381,765,523,203,441,259,715,284,870,552,429,381,750,838,764,496,720,162,249,742,450,276,789,464,634,901,319,465,571,660,595,200,000,000,000,000,000,00087!2,107,757,298,379,527,717,213,600,518,699,389,595,229,783,738,061,356,212,322,972,511,214,654,115,727,593,174,080,683,423,236,414,793,504,734,471,782,400,000,000,000,000,000,00088!185,482,642,257,398,439,114,796,845,645,546,284,380,220,968,949,399,346,684,421,580,986,889,562,184,028,199,319,100,141,244,804,501,828,416,633,516,851,200,000,000,000,000,000,00089!16,507,955,160,908,461,081,216,919,262,453,619,309,839,666,236,496,541,854,913,520,707,833,171,034,378,509,739,399,912,570,787,600,662,729,080,382,999,756,800,000,000,000,000,000,00090!1,485,715,964,481,761,497,309,522,733,620,825,737,885,569,961,284,688,766,942,216,863,704,985,393,094,065,876,545,992,131,370,884,059,645,617,234,469,978,112,000,000,000,000,000,000,00091!135,200,152,767,840,296,255,166,568,759,495,142,147,586,866,476,906,677,791,741,734,597,153,670,771,559,994,765,685,283,954,750,449,427,751,168,336,768,008,192,000,000,000,000,000,000,00092!12,438,414,054,641,307,255,475,324,325,873,553,077,577,991,715,875,414,356,840,239,582,938,137,710,983,519,518,443,046,123,837,041,347,353,107,486,982,656,753,664,000,000,000,000,000,000,00093!1,156,772,507,081,641,574,759,205,162,306,240,436,214,753,229,576,413,535,186,142,281,213,246,807,121,467,315,215,203,289,516,844,845,303,838,996,289,387,078,090,752,000,000,000,000,000,000,00094!108,736,615,665,674,308,027,365,285,256,786,601,004,186,803,580,182,872,307,497,374,434,045,199,869,417,927,630,229,109,214,583,415,458,560,865,651,202,385,340,530,688,000,000,000,000,000,000,00095!10,329,978,488,239,059,262,599,702,099,394,727,095,397,746,340,117,372,869,212,250,571,234,293,987,594,703,124,871,765,375,385,424,468,563,282,236,864,226,607,350,415,360,000,000,000,000,000,000,00096!991,677,934,870,949,689,209,571,401,541,893,801,158,183,648,651,267,795,444,376,054,838,492,222,809,091,499,987,689,476,037,000,748,982,075,094,738,965,754,305,639,874,560,000,000,000,000,000,000,00097!96,192,759,682,482,119,853,328,425,949,563,698,712,343,813,919,172,976,158,104,477,319,333,745,612,481,875,498,805,879,175,589,072,651,261,284,189,679,678,167,647,067,832,320,000,000,000,000,000,000,00098!9,426,890,448,883,247,745,626,185,743,057,242,473,809,693,764,078,951,663,494,238,777,294,707,070,023,223,798,882,976,159,207,729,119,823,605,850,588,608,460,429,412,647,567,360,000,000,000,000,000,000,00099!933,262,154,439,441,526,816,992,388,562,667,004,907,159,682,643,816,214,685,929,638,952,175,999,932,299,156,089,414,639,761,565,182,862,536,979,208,272,237,582,511,852,109,168,640,000,000,000,000,000,000,000100!93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000