Factorial (n!)

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Factorial definition formula
Recursive factorial formula
Striling’s approximation
Factorial table
C program for factorial calculation

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

$n!=\begin{Bmatrix}1 & ,n=0 \\ \prod_{k=1}^{n}k & ,n>0\end{matrix}” align=”absmiddle”></p> <p>For examples:</p> <p><span style=$ 1! = 1
2! = 1×2 = 2
3! = 1×2×3 = 6
4! = 1×2×3×4 = 24
5! = 1×2×3×4×5 = 120
6! = 1×2×3×4×5×6 = 720
7! = 1×2×3×4×5×6×7 = 5040

Recursive factorial formula

n! = n×(n-1)!

Striling’s approximation

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

For example:

7! ≈ √2π7 ⋅ 7⁷⋅e^-7= 5040

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 fact;

}