factorial

/fækˈtɔːɹi.əl/

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.

Noun

factorial (plural factorials)

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.
- The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and...1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428
- This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#92;prod#95;#123;k#61;1#125;ⁿk#61;1#92;cdot 2#92;cdot 3#92;cdotsn.But what does this equal?
  Well, of course we can say that...2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School, volume 47, number 4, page 40

Adjective

factorial (comparative more factorial, superlative most factorial)

Of or pertaining to a factor or factorial.
- I shall denote, as usual, the factorial product of the numbers up to n by n#33;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#33;#33;#61;n#92;cdot(n-2)#33;#33;.Starting with1#33;#33;#61;1,#92;quad...1903, Arthur Schuster, “On some Definite Integrals, and a New Method of Reducing a Function of Spherical Co-ordintes to a Series of Spherical Harmonics”, in Philosophical Transactions of the Royal...
- The definition of addition is an example of definition by induction, sometimes called recursive definition. As another example of this, consider the following inductive definition of the factorial function.
  We define n#33; for n#92;in#92;mathbbN by the following two properties,
  (i) 1#33; is defined...1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, →ISBN, page 21
Of or pertaining to a factor, a kind of business agent.
- The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted.2004, The Digest: Annotated British, Commonwealth, and European Cases
(dated) Of or pertaining to a factory.

factorial meaning in Tamil, Gujarati, Tagalog and Indonesian

factorial in Tamil

காரணீயம், சினையகம், காரணியம், தொடர் பெருக்கம்

factorial in Gujarati

factorial: ક્રમગુણિત kramguṇit

factorial in Tagalog

mathematical operation or its result: buuin

factorial in Indonesian

mathematical operation or its result: faktorial

More languagesFewer languages

factorial in Thai: แฟกทอเรียล
factorial in Vietnamese: giai thừa

Forms of factorial

Noun
plural	factorials
Adjective
comparative	more factorial
superlative	most factorial

Plural of factorial: factorials

Origin of factorial

From factor + -ial.

Words formed from factorial

Phrases with factorial

Words that rhyme with factorial

48 more rhymesFewer rhymes

Questions about factorial

What does factorial mean?: Factorial means 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.
What is factorial in Tamil?: Factorial in Tamil is காரணீயம், சினையகம், காரணியம். See Factorial meaning in Tamil.
What part of speech is factorial?: Factorial can be a noun or an adjective.
How do you pronounce factorial?: Factorial is pronounced /fækˈtɔːɹi.əl/.
What is the plural of factorial?: The plural of factorial is factorials.

Words near factorial in the dictionary

Adapted from Wiktionary: factorial (page history and authors); factorial (Tamil Wiktionary) (page history and authors); ક્રમગુણિત (Gujarati) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated: 2026-09-02

Pronunciation audio from Wikimedia Commons, each file under its own free license: LL-Q1860 (eng)-Vealhurl-factorial.wav.

Cite this entry: “factorial.” Word.ws, https://word.ws/factorial. Based on Wiktionary, CC BY-SA 4.0.