Factorial

The continued product of first n natural numbers is called the n factorial and is denoted by n!.

n! = 1 × 2 × 3 × 4 × … × (n − 1) × n

5! = 1 × 2 × 3 × 4 × 5 = 120

Zero Factorial

It does not make any sense to define it as the product of the integers from 1 to zero. So,

0! = 1

Deduction

n! = 1 × 2 × 3 × 4 × … × (n − 1) × n

= [1 × 2 × 3 × 4 × … × (n − 1)]n

n! = n(n − 1)!

For example, 8! = 8(7!)