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

![diagram](/math/algebra/factorial/factorial.GIF)

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

![diagram](/math/algebra/factorial/sriling.GIF)

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;


							

}