Factorial

the multiplication of a series of consecutive numbers from I to n inclusive, where n is a whole number. Thus, factorial 5, written as 5! = 1 x 2 x 3 x 4 x 5 = 120. Factorials of much larger numbers are not usually defined.

Taken from Dictionary of Science

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In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

and

The notation n! was introduced by Christian Kramp in 1808.

The factorial function can also be defined for non-integer values, which involves more advanced mathematics, especially mathematical analysis.

Taken from Wikipedia