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# What is the factorial of a number?

A factorial is the product of consecutive natural numbers for all integers greater than or equal to 0. Factorials usually start with 1; the symbol for factorial is an exclamation point (!). For example, 4 factorial (4!) is 1 × 2 × 3 × 4, or 24. In the numerical system, consecutive factorials are 1 (1! = 1), 2 (2! = 1 × 2), 6 (3! = 1 × 2 × 3), 24 (4! = 1 × 2 × 3 × 4), 120 (5! = 1 × 2 × 3 × 4 × 5), 720 (6! = 1 × 2 × 3 × 4 × 5 × 6), 5040 (7! = 1 × 2 × 3 × 4 × 5 × 6 × 7), 40,320 (8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8), 362,880 (9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9), and so on.

There are two additional rules: The number 0 factorial (0!) = 1; and the factorial values for negative integers are not defined. Factorials are most often used in reference to counting numbers, statistics (especially in probability calculations), calculus, and physics.

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