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

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.

Other Word Forms

• factorially adverb

Word History and Origins

Origin of factorial¹

First recorded in 1810–20; factor + -ial

Example Sentences

The healthiness of skin is multi factorial – lifestyle, environment, stress levels, diet and exercise regime all play into how our skin ages.

From BBC

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