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.