[fak-tawr-ee-uh l, -tohr-]


Mathematics. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24. Symbol: n!, where n is the given integer.


Mathematics. of or relating to factors or factorials.
of or relating to a factor or a factory.

Origin of factorial

First recorded in 1810–20; factor + -ial
Related formsfac·to·ri·al·ly, adverb
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

Examples from the Web for factorial

Historical Examples of factorial

  • The possible connections within it were factorial one hundred thousand.

    Unwise Child

    Gordon Randall Garrett

  • It is by no means unlikely that various dark forms of lubricipeda correspond with a progressive series of factorial additions.

    Problems of Genetics

    William Bateson

  • These phenomena demonstrate the existence of a complex interrelation between the factorial units.

  • In its place stands the factorial hypothesis, evolved by workers in America, England, and France at about the same time.

    Applied Eugenics

    Paul Popenoe and Roswell Hill Johnson

British Dictionary definitions for factorial



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


of or involving factorials or factors
Derived Formsfactorially, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for factorial

1816 (n.), 1837 (adj.), from factor + -al (2).

Online Etymology Dictionary, © 2010 Douglas Harper

factorial in Science



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 X 2 X 3 X 4, or 24.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.