The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers.This is writtenN! = N * (N-1) * (N-2) * ... * 1.The factorial of zero is one because it is an {empty product}.Factorial can be defined recursively as0! = 1 N! = N * (N-1)! , N > 0The gamma function is the equivalent for real numbers.(2005-01-07)