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The factorials up to 10

1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000.

__Distribution of the remainders__ when the numbers in this family are divided by *n*=2, 3,..., 11. (I took into account 6000 values, from 1 to 6000!).

n\r | 0 | 1 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2 | 5999 | 1 | 2 | ||||||||

3 | 5998 | 1 | 1 | 3 | |||||||

4 | 5997 | 1 | 2 | 0 | 4 | ||||||

5 | 5996 | 2 | 1 | 0 | 1 | 5 | |||||

6 | 5998 | 1 | 1 | 0 | 0 | 0 | 6 | ||||

7 | 5994 | 2 | 1 | 1 | 0 | 0 | 2 | 7 | |||

8 | 5997 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 8 | ||

9 | 5995 | 1 | 1 | 1 | 0 | 0 | 2 | 0 | 0 | 9 | |

10 | 5996 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 10 |

11 | 5990 | 2 | 3 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 2 |

Imagine to divide the members of this family by a number *n* and compute the remainders. Should they be uniformly distributed, each remainder from 0 to *n*-1 would be obtained in about (1/*n*)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/*n*.

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