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

$n!=\begin{Bmatrix}1 & ,n=0 \\ \prod_{k=1}^{n}k & ,n>0\end{matrix}$

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

n! = n×(n-1)!

Example:

5! = 5×(5-1)! = 5×4! = 5×24 = 120

$n!\approx \sqrt{2\pi n}\cdot n^n\cdot e^{-n}$

Example:

5! ≈ √2π5⋅5⁵⋅e^-5= 118.019

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 fact;

}