Factorial

If you want to calculate a factorial use the iterative algorithm. The recursive algorithm is included because factorial highlights the differences between iterating and recursing nicely.

Iterative

$$n!=\prod_{k=1}^n k \!$$

Recursive

$$n! = \begin{cases} 1 & \text{if } n = 0, \\ (n-1)!\times n & \text{if } n > 0. \end{cases}$$