# Factorial Is a math shorthand indicating a number that is a product of all numbers from 1 to n. $ \begin {align} n! &= \prod_{a=1}^{n}{a} \\ 0! &= 1 \end {align} $ ## Properties $(n+1)! - n! = n \cdot n!$ Because: $ \begin{align} (n+1)! - n! &= (n+1)n! - n! \\ &= n! \cdot ((n+1) - 1) \\ &= n \cdot n! \end{align}