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: Noun 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, "Prime Gap Grows After Decades-Long Lull," 10 Dec. 2014

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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Time Traveler for factorial

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The first known use of factorial was in 1837

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Cite this Entry

“Factorial.” The Merriam-Webster.com Dictionary, Merriam-Webster Inc., https://www.merriam-webster.com/dictionary/factorial?pronunciation&lang=en_us&dir=f&file=factor07. Accessed 28 January 2020.

More from Merriam-Webster on factorial

Rhyming Dictionary: Words that rhyme with factorial

Britannica.com: Encyclopedia article about factorial

Comments on factorial

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showing steady, earnest care and effort

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