factorial
1 of 2adjective
fac·to·ri·al fak-ˈtȯr-ē-əl 
: of, relating to, or being a factor or a factorial
factorial
2 of 2noun
1
: the product of all the positive integers from 1 to n —symbol n!
2
: the quantity 0! arbitrarily defined as equal to 1
Example Sentences
Recent Examples on the Web
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 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 Here’s one easy way to construct a list of, say, 100 composite numbers in a row: Start with the numbers 2, 3, 4, … , 101, and add to each of these the number 101 factorial (the product of the first 101 numbers, written 101!). Quanta Magazine, 10 Dec. 2014 See More
Adjective
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
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 Here’s one easy way to construct a list of, say, 100 composite numbers in a row: Start with the numbers 2, 3, 4, … , 101, and add to each of these the number 101 factorial (the product of the first 101 numbers, written 101!). Quanta Magazine, 10 Dec. 2014 See More Word History
Etymology
Adjective
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
Adjective
1837, in the meaning defined above
Noun
1869, in the meaning defined at sense 1