# Factorial

[fak-tawr-ee-uh l, -tohr-] /fækˈtɔr i əl, -ˈtoʊr-/

**noun**

1.

Mathematics. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24. Symbol: n!, where n is the given integer.

**adjective**

2.

Mathematics. of or relating to or factorials.

3.

of or relating to a or a factory.

/fækˈtɔːrɪəl/

**noun**

1.

the product of all the positive integers from one up to and including a given integer. Factorial zero is assigned the value of one: factorial four is 1 × 2 × 3 × 4. Symbol: n!, where n is the given integer

**adjective**

2.

of or involving factorials or factors

1816 (n.), 1837 (**adj.**), from factor + -al (2).

factorial

(fāk-tôr’ē-əl)

The product of all of the positive integers from 1 to a given positive integer. It is written as the given integer followed by an exclamation point. For example, the factorial of 4 (written 4!) is 1 × 2 × 3 × 4, or 24.

mathematics

The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written

N! = N * (N-1) * (N-2) * … * 1.

The factorial of zero is one because it is an empty product.

Factorial can be defined recursively as

0! = 1 N! = N * (N-1)! , N > 0

The gamma function is the equivalent for real numbers.

(2005-01-07)

Tagged: f

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