factorial

[ fak-tawr-ee-uhl, -tohr- ]

noun

1. Mathematics. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24. : n!, where n is the given integer.

adjective

1. Mathematics. of or relating to factors or factorials.
2. of or relating to a factor or a factory.

factorial

/ fækˈtɔːrɪəl /

noun

1. 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

adjective

1. of or involving factorials or factors

factorial

/ făk-tôr′ē-əl /

1. 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.

Derived Forms

• facˈtorially, adverb

Other Words From

• fac·tori·al·ly adverb

Word History and Origins

Origin of factorial¹

First recorded in 1810–20; factor + -ial

Example Sentences

The exclamation point is of course the factorial symbol, not an expression of excitement about numbers.

From Scientific American

The expression n! — “n factorial,” when said aloud — describes the product of multiplying all the integers from 1 to n.

From New York Times

The odds the cards would be in whatever order you wrote down are 1 in 52 factorial, which is 80658175170943878571660636856403766975289505440883277824000000000000.

From Washington Post

John Nash, the world-renowned mathematician, died; Left us too early but in recognition, I’d Put age of death on his graveside memorial: 10 squared times 2, plus 6, less 5 factorial.

From Washington Post

We incubated a natural diatom community from coastal New Zealand waters in a short-term incubation experiment using a factorial matrix of temperature and CO2, and measured effects on community structure.

From New York Times