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[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
1810-20; factor + -ial
Related forms
factorially, adverb Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2017.
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Examples from the Web for factorial
Historical Examples
  • The possible connections within it were factorial one hundred thousand.

    Unwise Child Gordon Randall Garrett
  • These phenomena demonstrate the existence of a complex interrelation between the factorial units.

  • 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
  • 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 Forms
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
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Word Origin and History for factorial

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

Online Etymology Dictionary, © 2010 Douglas Harper
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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 × 2 × 3 × 4, or 24.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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factorial in Technology

The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an empty product.
Factorial can be defined recursively as
0! = 1 N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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