[ fak-tawr-ee-uh l, -tohr- ]
/ fækˈtɔr i əl, -ˈtoʊr- /


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


fac·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

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

    Unwise Child|Gordon Randall Garrett

British Dictionary definitions for factorial

/ (fækˈtɔːrɪəl) maths /


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 forms of factorial

factorially, 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

Science definitions for factorial

[ făk-tôrē-əl ]

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.