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factorial

Also known as factorial function, !, n!, Factorial function, Factorials, Factorial number, ! (math)

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A factorial is a mathematical operation where you multiply a number by every positive whole number below it—for example, 5 factorial (written as 5!) equals 5 × 4 × 3 × 2 × 1, which equals 120. Factorials grow very rapidly and are useful in mathematics for counting arrangements and combinations of objects.

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Wikidata facts

Image: Factorial 1-5.png

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Stack Exchange tag: math.stackexchange.com/tags/factorial
Commons category: Factorial (function)
described at URL: www.w3.org/TR/MathML3/chapter4.html#contm.factorial

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~30 min read

Article

12 sections

Contents

History
Definition
Factorial of zero
Applications
Properties
Growth and approximation
Divisibility and digits
Continuous interpolation and non-integer generalization
Computation
Related sequences and functions
References
External links

{| class="wikitable" style="margin:0 0 0 1em; text-align:right; float:right;" |+ Selected factorials; values in scientific notation are rounded |- ! n ! n! |- | 0 || 1 |- | 1 || 1 |- | 2 || 2 |- | 3 || 6 |- | 4 || 24 |- | 5 || 120 |- | 6 || 720 |- | 7 || |- | 8 || |- | 9 || |- | 10 || |- | 11 || |- | 12 || |- | 13 || |- | 14 || |- | 15 || |- | 16 || |- | 17 || |- | 18 || |- | 19 || |- | 20 || |- | 25 | style="text-align:left" | |- | 50 | style="text-align:left" | |- | 52 | style="text-align:left" | |- | 70 | style="text-align:left" | |- | 100 | style="text-align:left" | |- | 450 | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:left" | |- | | style="text-align:right" | 10 |- | || 10 |- | || 10 |- | || 10 |- | googol| || 10 |- | || 10 |}

In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: