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
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
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
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Adjective
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
Cite this Entry
“Factorial.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/factorial. Accessed 15 Jul. 2025.
Copy CitationKids 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
2 of 2 adjective
: of, relating to, or being a factor or factorial
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