Factorial
/fækˈtɔriəl/Definition, CEFR level C1, pronunciation, examples, and quiz.
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Definition
adjectiveRelated to multiplying a whole number by all smaller positive numbers.
Extra definitions
noun; adjectiveThe product of integers up to a number.
noun; adjectiveRelating to factorial calculations.
noun; adjectiveA function written with an exclamation mark.
Sentence Examples
The factorial of five is 120.
We practiced factorial problems.
The program calculates factorial values.
Synonyms & Antonyms
Synonyms:
None
Antonyms:
None
Word Origin & History
Proto-Indo-European *h₂el-der.?
Literary Quotations & Historical Citations
“The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inclusive.”
— 1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428:
“This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#92;prod#95;#123;k#61;1#125;ⁿk#61;1#92;cdot 2#92;cdot 3#92;cdotsn.But what does this equal? Well, of course we can say that it is equal to n factorial and write#92;prod#95;#123;k#61;1#125;ⁿk#61;n#33; and then use our calculators, but inventing a new symbol like 'factorial' feels like an admission of defeat!”
— 2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School, volume 47, number 4, page 40:
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CEFR Practice Quiz
The ____ of five is 120.