# Definitions for **factorial**fækˈtɔr i əl, -ˈtoʊr-

### This page provides all possible meanings and translations of the word **factorial**

### Random House Webster's College Dictionary

fac•to•ri•alfækˈtɔr i əl, -ˈtoʊr-(n.)

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.

**Category:**Math(adj.)of or pertaining to factors or factorials.

**Category:**Mathof or pertaining to a factor or a factory.

#### Origin of **factorial**:

1810–20

fac•to′ri•al•ly(adv.)

### Princeton's WordNet

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

### Wiktionary

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.

### Webster Dictionary

Factorial(adj)

of or pertaining to a factory

Factorial(adj)

related to factorials

Factorial(noun)

a name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x).F(x + h).F(x + 2h) . . . F[x + (n-1)h] is called a factorial term, and its several factors take the name of factorials

Factorial(noun)

the product of the consecutive numbers from unity up to any given number

### Freebase

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.

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"factorial." *Definitions.net.* STANDS4 LLC, 2014. Web. 17 Sep. 2014. <http://www.definitions.net/definition/factorial>.