Factorial (n!)

The factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.

For n>0,

n! = 1×2×3×4×...×n

For n=0,

0! = 1

Factorial definition formula

Examples:

1! = 1

2! = 1×2 = 2

3! = 1×2×3 = 6

4! = 1×2×3×4 = 24

5! = 1×2×3×4×5 = 120

Recursive factorial formula

n! = n×(n-1)!

Example:

5! = 5×(5-1)! = 5×4! = 5×24 = 120

Striling's approximation

Example:

5! ≈ √2π5·5⁵·e^-5 = 118.019

Factorial table

Number n	Factorial n!
0	1
1	1
2	2
3	6
4	24
5	120
6	720
7	5040
8	40320
9	362880
10	3628800
11	3.991680x107
12	4.790016x108
13	6.227021x109
14	8.717829x1010
15	1.307674x1012
16	2.092279x1013
17	3.556874x1014
18	6.402374x1015
19	1.216451x1017
20	2.432902x1018

C program for factorial calculation

double factorial(unsigned int n)

{

    double fact=1.0;

   

    if( n > 1 )

        for(unsigned int k=2; k<=n; k++)

            fact = fact*k;

 

    return f;

}

 

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See also

• Factorial calculator
• Logarithm
• Factorial - Wikipedia