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factorials
The factorial of an integer  $n0$">, denoted by n!, is the product of all the integers from 1 to  $n$. By definition,  $0! =1$.

For example,  $6! = 1\cdot2\cdot3\cdot4\cdot5\cdot6=720$.

The number of permutations of  $n$  objects is  $n!$.

Factorials are involved in many classic formulas, like

\[\sum_{k=0}^{\infty}\frac{1}{k!}=e,\quad\quad \sum_{k=0}^{\infty}(-1)^k\frac{1}{k!}=\frac{1}{e}\,.\]

The first factorials are 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of factorials
Useful links Mathworld, Factorial
Wikipedia, Factorial
OEIS, sequence A000142
Factorials can also be... (you may click on names or numbers)

ABA 24 aban 24 120 720 abundant 24 120 720 5040 40320 362880 3628800 39916800 admirable 24 120 amenable 24 120 720 5040 40320 362880 3628800 39916800 479001600 apocalyptic 720 binomial 120 compositorial 24 congruent 24 120 720 40320 362880 3628800 constructible 24 120 Cunningham 24 120 5040 d-powerful 24 dig.balanced 120 3628800 economical 362880 3628800 equidigital 362880 3628800 eRAP 24 Eulerian 120 evil 24 120 720 5040 40320 362880 479001600 gapful 120 40320 362880 3628800 39916800 479001600 6227020800 87178291200 Harshad 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 hexagonal 120 highly composite 24 120 720 5040 iban 24 120 720 40320 idoneal 24 120 inconsummate 362880 interprime 120 3628800 Jordan-Polya 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 katadrome 720 lonely 120 Lynch-Bell 24 metadrome 24 nialpdrome 720 nonagonal 24 nude 24 oban 720 odious 3628800 39916800 panconsummate 24 pandigital 120 pernicious 24 3628800 plaindrome 24 practical 24 120 720 5040 40320 362880 3628800 pseudoperfect 24 120 720 5040 40320 362880 Ruth-Aaron 24 super Niven 24 120 5040 40320 superabundant 24 120 720 5040 tau 24 720 5040 40320 362880 3628800 39916800 479001600 tetrahedral 120 triangular 120 tribonacci 24 trimorphic 24 Ulam 720 unprimeable 5040 40320 362880 3628800 untouchable 120 40320 362880 wasteful 24 120 720 5040 40320 Zuckerman 24 Zumkeller 24 120 720 5040 40320