# factorial

1 of 2

fac·​to·​ri·​al
: of, relating to, or being a factor or a factorial

factorial

2 of 2

## noun

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
If each neuron, or brain cell, could connect with any other in your skull, the number of combinations would be 85 billion factorial. Bob Berman, Discover Magazine, 3 June 2014 The factorial growth of these particle physics calculations outpaces the exponential growth of computing power. Quanta Magazine, 1 Dec. 2022 Afterwards, the effect of changing the amount of four components (the amount of primary surfactant, the essence, the hydratant and the colouring agent) of the bubble bath was studied by a fractional factorial design. Ncbi Rofl, Discover Magazine, 8 Dec. 2011 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
Noun
But as this number grows, the possible routes increase at a rate that depends on n!, the factorial of the number of cities. The Physics Arxiv Blog, Discover Magazine, 30 July 2024 Even computers have a hard time evaluating the formula, especially for large values of n. Among other things, the factorial is part of the problem: the values quickly become extremely large, and the calculations require a lot of computing power. Manon Bischoff, Scientific American, 16 Nov. 2023 The exclamation point denotes an arithmetic operation known as a factorial, which multiplies all natural numbers up to the number before the factorial. Manon Bischoff, Scientific American, 16 Nov. 2023 The next factorial is 4! Eugenia Cheng, WSJ, 21 Apr. 2022 The problem scales as a factorial, a mathematical relationship that grows even faster than exponential growth. Quanta Magazine, 1 Dec. 2022 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

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'factorial.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

Etymology

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

Noun

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

First Known Use

1837, in the meaning defined above

Noun

1869, in the meaning defined at sense 1

Time Traveler
The first known use of factorial was in 1837

factorial

## Cite this Entry

“Factorial.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/factorial. Accessed 8 Sep. 2024.

## Kids Definition

factorial

1 of 2 noun
fac·​to·​ri·​al fak-ˈtōr-ē-əl
-ˈtȯr-
1
: the product of all the positive whole numbers from 1 to the number given
symbol !
2
: the quantity 0! that is defined as equal to 1

factorial