Definition
Factorial
The factorial n! is a countdown product from n to 1, with 0! defined as 1.
What it means
Factorial is a countdown product. Start at the number, multiply by each smaller positive whole number, and stop at 1. The special starting case is 0! = 1.
Remember it
Count down, multiply, stop at 1.
Example
4! = 4 × 3 × 2 × 1 = 24. This is also the number of different ways to arrange four distinct objects in a row.
Watch for
The exclamation mark is part of the notation: 5! means factorial, not excitement. Also, 0! is 1.
Common mix-up
5! is not 5 × 5 and not 5 + 4 + 3 + 2 + 1.
Exact meaning
For a non-negative integer n, the factorial n! is n × (n − 1) × ··· × 2 × 1 when n ≥ 1; by definition, 0! = 1.