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

See Examples For:

factorial

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

The exclamation point is not punctuation here; it indicates the factorial notation.

From Textbooks ● May 6, 2020

The odds the cards would be in whatever order you wrote down are 1 in 52 factorial, which is 80658175170943878571660636856403766975289505440883277824000000000000.

From Washington Post ● Apr. 21, 2019

Since each term contains a factorial, apply the ratio test.

From Textbooks ● Mar. 30, 2016

Factor analysis; a synthesis of factorial methods, by Karl J. Holzinger & Harry H. Harman. © 11Nov41; A159487.

From U.S. Copyright Renewals, 1969 July - December by Library of Congress. Copyright Office