What is the value of 4 factorial (4!)?

The value of 4 factorial, written 4!, is 24. Factorial means multiplying a whole number by every positive integer below it, so 4! = 4 × 3 × 2 × 1 = 24.

Factorials appear throughout mathematics, especially in counting and probability. For example, four distinct objects can be arranged in 4! different orders: 24 permutations. Factorials also appear in formulas for combinations, binomial expansions, series, and many areas of statistics and computer science.

The exclamation mark is an operator here, not punctuation showing excitement. Another common mistake is to calculate 4 × 3 and stop at 12, or to use 4 × 4 and get 16. The definition includes every positive integer down to 1. By convention, 0! is also equal to 1, because that value makes many counting formulas work consistently. Factorials grow very rapidly: 5! is 120 and 6! is 720.