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.

---

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

---

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.

---

Other Word 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

A factorial is the product of a positive integer and all the positive integers below it.

From Textbooks • Dec. 21, 2021

Before we get to that, we need to introduce some more factorial notation.

From Textbooks • May 6, 2020

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

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.