# 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}