factorialfækˈtɔr i əl, -ˈtoʊr-

**factorial** (n)

- plural
- factorial / adj

### English Definitions:

#### factorial (adj)

the product of all the integers up to and including a given integer

"1, 2, 6, 24, and 120 are factorials"

#### factorial (adj)

of or relating to factorials

#### factorial (Noun)

The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 * 2 * 3 * 4 * 5 = 120.

#### factorial (Adjective)

Of or pertaining to a factor or factorial.

#### factorial (Adjective)

Of or pertaining to a factor.

#### factorial (Adjective)

Of or pertaining to a factory.

#### Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product. The factorial operation is encountered in many different areas of mathematics, notably in combinatorics, algebra and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence. This fact was known at least as early as the 12th century, to Indian scholars. The notation n! was introduced by Christian Kramp in 1808. The definition of the factorial function can also be extended to non-integer arguments, while retaining its most important properties; this involves more advanced mathematics, notably techniques from mathematical analysis.

#### Factorial

In mathematics, the factorial of a non-negative integer n {\displaystyle n} , denoted by n ! {\displaystyle n!} , is the product of all positive integers less than or equal to n {\displaystyle n} . The factorial of n {\displaystyle n} also equals the product of n {\displaystyle n} with the next smaller factorial:

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