# What is factorial? How to calculate factorial of a number?

Definition of factorial

The factorial is the product of an integer and all the integers below it; e.g. factorial four ( 4! ) is equal to 24 (4 x 3 x 2 x 1). The factorial value of 0 is by definition equal to 1. For negative integers, factorials are not defined. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 x 2 x 1). The factorial symbol is the exclamation mark (!).

The factorial formula

If n is an natural number greater than or equal to 1, then n! = n x (n - 1) x (n - 2) x (n - 3) ... 3 x 2 x 1

If p = 0, then p! = 1 by convention.

Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Table of Factorials

n n!
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 39916800
12 479001600
13 6227020800
14 87178291200
15 1307674368000
16 20922789888000
17 355687428096000
18 6402373705728000
19 121645100408832000
20 2432902008176640000
21 51090942171709440000
22 1124000727777607680000
23 25852016738884976640000
24 620448401733239439360000
25 15511210043330985984000000
26 403291461126605635584000000
27 10888869450418352160768000000
28 304888344611713860501504000000
29 8841761993739701954543616000000
30 265252859812191058636308480000000