fac·​to·​ri·​al | \ fak-ˈtȯr-ē-əl How to pronounce factorial (audio) \

Definition of factorial

 (Entry 1 of 2)

: of, relating to, or being a factor or a factorial



Definition of factorial (Entry 2 of 2)

1 : the product of all the positive integers from 1 to n symbol n!
2 : the quantity 0! arbitrarily defined as equal to 1

Examples of factorial in a Sentence

Recent Examples on the Web: Adjective The benefits of having a small and independent unit focusing on a challenge is multi-factorial. Nelson Dumas, Forbes, 24 June 2022 The coefficients of all those polynomials were only made up of odd factorial denominators with their alternating signs. Quanta Magazine, 1 June 2022 The total number of possibilities is 5 x 4 x 3 x 2 x 1 or 120, the factorial 5!. Eugenia Cheng, WSJ, 21 Apr. 2022 Recent Examples on the Web: Noun Factorials grow so fast that a library of 240 songs will result in sequences totaling the figure 240!—a factorial that is a mind-boggling 469 digits long. Eugenia Cheng, WSJ, 21 Apr. 2022 The exclamation point there isn’t the end of a sentence but, instead, denotes a factorial, the value obtained by multiplying the number by every number that precedes it. Philip Bump, Washington Post, 20 Dec. 2019 But for graphs with n nodes, the number of different matchings is n factorial (1 * 2 * 3 * … * n), which is so much larger than n that this brute-force approach is hopelessly impractical for all but the smallest graphs. Quanta Magazine, 14 Dec. 2015 Here’s one easy way to construct a list of, say, 100 composite numbers in a row: Start with the numbers 2, 3, 4, … , 101, and add to each of these the number 101 factorial (the product of the first 101 numbers, written 101!). Quanta Magazine, 10 Dec. 2014 See More

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'factorial.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

First Known Use of factorial


1837, in the meaning defined above


1869, in the meaning defined at sense 1

History and Etymology for factorial


factor entry 1 + -ial (in mathematical sense after French factoriel)


borrowed from French factorielle, noun derivative from feminine of factoriel factorial entry 1

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The first known use of factorial was in 1837

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Dictionary Entries Near factorial

factor group



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Last Updated

6 Jul 2022

Cite this Entry

“Factorial.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/factorial. Accessed 13 Aug. 2022.

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More from Merriam-Webster on factorial

Britannica.com: Encyclopedia article about factorial


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