Факториал натурального числа n (обозначение – “n!“) равен произведению всех натуральных чисел от 1 до n включительно.
n! = 1 * 2 * 3 * 4 … * n
Ниже представлены таблицы с факториалами чисел от 1 до 20 (точные значения) и от 21 до 100 (приближенные значения).
1. Факториалы чисел от 1 до 20
(n!) | Значение |
| 1! | 1 |
| 2! | 2 |
| 3! | 6 |
| 4! | 24 |
| 5! | 120 |
| 6! | 720 |
| 7! | 5040 |
| 8! | 40320 |
| 9! | 362880 |
| 10! | 3628800 |
| 11! | 39916800 |
| 12! | 479001600 |
| 13! | 6227020800 |
| 14! | 87178291200 |
| 15! | 1307674368000 |
| 16! | 20922789888000 |
| 17! | 355687428096000 |
| 18! | 6402373705728000 |
| 19! | 121645100408832000 |
| 20! | 2432902008176640000 |
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2. Факториалы чисел от 21 до 100
Факториал – это быстрорастущая функция, и начиная с определенного n значения достаточно велики. Поэтому в математических вычислениях удобнее пользоваться приближенными значениями для больших чисел.
(n!) | |
| 21! | 5,10909 ⋅ 1019 |
| 22! | 1,124 ⋅ 1021 |
| 23! | 2,5852 ⋅ 1022 |
| 24! | 6,20448 ⋅ 1023 |
| 25! | 1,55112 ⋅ 1025 |
| 26! | 4,03291 ⋅ 1026 |
| 27! | 1,08889 ⋅ 1028 |
| 28! | 3,04888 ⋅ 1029 |
| 29! | 8,84176 ⋅ 1030 |
| 30! | 2,65253 ⋅ 1032 |
| 31! | 8,22284 ⋅ 1033 |
| 32! | 2,63131 ⋅ 1035 |
| 33! | 8,68332 ⋅ 1036 |
| 34! | 2,95233 ⋅ 1038 |
| 35! | 1,03331 ⋅ 1040 |
| 36! | 3,71993 ⋅ 1041 |
| 37! | 1,37638 ⋅ 1043 |
| 38! | 5,23023 ⋅ 1044 |
| 39! | 2,03979 ⋅ 1046 |
| 40! | 8,15915 ⋅ 1047 |
| 41! | 3,34525 ⋅ 1049 |
| 42! | 1,40501 ⋅ 1051 |
| 43! | 6,04153 ⋅ 1052 |
| 44! | 2,65827 ⋅ 1054 |
| 45! | 1,19622 ⋅ 1056 |
| 46! | 5,50262 ⋅ 1057 |
| 47! | 2,58623 ⋅ 1059 |
| 48! | 1,24139 ⋅ 1061 |
| 49! | 6,08282 ⋅ 1062 |
| 50! | 3,04141 ⋅ 1064 |
| 51! | 1,55112 ⋅ 1066 |
| 52! | 8,06582 ⋅ 1067 |
| 53! | 4,27488 ⋅ 1069 |
| 54! | 2,30844 ⋅ 1071 |
| 55! | 1,26964 ⋅ 1073 |
| 56! | 7,10999 ⋅ 1074 |
| 57! | 4,05269 ⋅ 1076 |
| 58! | 2,35056 ⋅ 1078 |
| 59! | 1,38683 ⋅ 1080 |
| 60! | 8,32099 ⋅ 1081 |
| 61! | 5,0758 ⋅ 1083 |
| 62! | 3,147 ⋅ 1085 |
| 63! | 1,98261 ⋅ 1087 |
| 64! | 1,26887 ⋅ 1089 |
| 65! | 8,24765 ⋅ 1090 |
| 66! | 5,44345 ⋅ 1092 |
| 67! | 3,64711 ⋅ 1094 |
| 68! | 2,48004 ⋅ 1096 |
| 69! | 1,71122 ⋅ 1098 |
| 70! | 1,1979 ⋅ 10100 |
| 71! | 8,5048 ⋅ 10101 |
| 72! | 6,1234 ⋅ 10103 |
| 73! | 4,4701 ⋅ 10105 |
| 74! | 3,3079 ⋅ 10107 |
| 75! | 2,4809 ⋅ 10109 |
| 76! | 1,8855 ⋅ 10111 |
| 77! | 1,4518 ⋅ 10113 |
| 78! | 1,1324 ⋅ 10115 |
| 79! | 8,9462 ⋅ 10116 |
| 80! | 7,1569 ⋅ 10118 |
| 81! | 5,7971 ⋅ 10120 |
| 82! | 4,7536 ⋅ 10122 |
| 83! | 3,9455 ⋅ 10124 |
| 84! | 3,3142 ⋅ 10126 |
| 85! | 2,8171 ⋅ 10128 |
| 86! | 2,4227 ⋅ 10130 |
| 87! | 2,1078 ⋅ 10132 |
| 88! | 1,8548 ⋅ 10134 |
| 89! | 1,6508 ⋅ 10136 |
| 90! | 1,4857 ⋅ 10138 |
| 91! | 1,352 ⋅ 10140 |
| 92! | 1,2438 ⋅ 10142 |
| 93! | 1,1568 ⋅ 10144 |
| 94! | 1,0874 ⋅ 10146 |
| 95! | 1,033 ⋅ 10148 |
| 96! | 9,9168 ⋅ 10149 |
| 97! | 9,6193 ⋅ 10151 |
| 98! | 9,4269 ⋅ 10153 |
| 99! | 9,3326 ⋅ 10155 |
| 100! | 9,3326 ⋅ 10157 |
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