## factorial

The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written

N! = N * (N-1) * (N-2) * ... * 1.

The factorial of zero is one because it is an empty product.

Factorial can be defined recursively as

0! = 1 N! = N * (N-1)! , N > 0

The gamma function is the equivalent for real numbers.

For example, the number of ways of shuffling 52 playing cards is 52! or nearly 10^68. 52 Factorial.