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factorial

File:Mplwp_factorial_stirling_loglog2.svg · Wikimedia Commons · See Wikimedia Commons

EntityQ120976· pop 86· linked from 555 articles

factorial

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

{| 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" |

AI overview

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.

AI-generated from the Wikipedia summary — may contain errors.

In the Vinony graph

Within Vinony's link graph, factorial is referenced by 555 other articles, and connects out to calculus, integral and derivative.

Vinony files it under Combinatorics, Factorial and binomial topics and Gamma and related functions.

Its subject is documented across 84 Wikipedia language editions.

Wikidata facts

Instance of
integer sequence
Image
Factorial 1-5.png
Show 8 more facts
Stack Exchange tag
math.stackexchange.com/tags/factorial
Commons category
Factorial (function)
described at URL
www.w3.org/TR/MathML3/chapter4.html#contm.factorial
different from
gamma function
topic's main category
Category:Factorial and binomial topics
on focus list of Wikimedia project
Wikipedia:Vital articles/Level/4
studied by
number theory
maintained by WikiProject
WikiProject Mathematics
Sources (3)

via Wikidata · CC0

~30 min read

Encyclopedic overview

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:

Excerpted from Wikipedia’s “factorial” article, available under the CC BY-SA 4.0 licence.

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Categories

CombinatoricsFactorial and binomial topicsGamma and related functionsUnary operations