factorial

American  

[fak-tawr-ee-uhl, -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. n!, where n is the given integer.

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adjective

1. Mathematics. of or relating to factors or factorials.

2. of or relating to a factor or a factory.

factorial British  

/ 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

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adjective

1. of or involving factorials or factors

factorial Scientific  

/ făk-tôr′ē-əl /

1. 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.

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Other Word Forms

Derived Forms

• factorially
  adverb

Etymology

Origin of factorial

First recorded in 1810–20; factor + -ial

Example Sentences

The healthiness of skin is multi factorial – lifestyle, environment, stress levels, diet and exercise regime all play into how our skin ages.

From BBC • Aug. 23, 2025

John Nash, the world-renowned mathematician, died; Left us too early but in recognition, I’d Put age of death on his graveside memorial: 10 squared times 2, plus 6, less 5 factorial.

From Washington Post • Jan. 28, 2016

Because Pedro, despite technically being part of the city of Los Angeles, is in spirit a peninsular community, Ibarra's book turns into something more than another fanboy factorial.

From Los Angeles Times • Jul. 2, 2015

Notice that, since factorials grow very quickly, the presence of the factorial term in the denominator results in the denominator becoming much larger than the numerator as increases.

From Textbooks • Feb. 13, 2015

Esp. appropriate for algorithms with factorial or super-exponential running time in the average case and probabilistically infinite worst-case running time.

From The Jargon File, Version 4.2.2, 20 Aug 2000 by Steele, Guy L.