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Difference between revisions of "Factorial number"

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(see also Factorial prime)
 
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In [[mathematics]] symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it.
 
In [[mathematics]] symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it.
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==Definition==
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A factorial is defined by the product
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:<math>n!  = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math>
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for <math>n \ge 1</math>.
 +
 +
The same written as mathmatical product
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:<math>n!  = \prod_{i = 1}^n i.</math>
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and as recurrence relation
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:<math> n! = n \cdot (n-1)!</math>
  
 
==Examples==
 
==Examples==
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:10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800
 
:10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800
  
Factorial numbers are those that are thus produced (in the cases above 120 and 362800 are factorial numbers.)
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==See also==
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*[[Factorial prime]]
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*[[Multifactorial number]]
  
 
==External links==
 
==External links==
*[https://en.wikipedia.org/wiki/Factorial Wikipedia]
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*[[Wikipedia:Factorial|Factorial]]
[[Category:Math]]
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[[Category:Number]]

Latest revision as of 13:40, 5 November 2023

In mathematics symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all whole numbers smaller than it.

Definition

A factorial is defined by the product

[math]\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }[/math]

for [math]\displaystyle{ n \ge 1 }[/math].

The same written as mathmatical product

[math]\displaystyle{ n! = \prod_{i = 1}^n i. }[/math]

and as recurrence relation

[math]\displaystyle{ n! = n \cdot (n-1)! }[/math]

Examples

5! = 5 * 4 * 3 * 2 * 1 = 120
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800

See also

External links