The product of a non-negative integer and all the integers below it is called the factorial.

The term factorial is related to factors which are multiplying elements. So, the factorial of a number represents the product of the number and all the numbers below to that number but all the numbers are positive integers except zero.

Exclamation mark (!) is used to denote the factorial operation in mathematics. It is written after the integer.

For example, let us find the value of $5!$.

$5! = 5 \times 4 \times 3 \times 2 \times 1$

The factorial symbol represents the product of all the numbers which are below a particular number.

$\implies 5! = 120$

Observe the following examples for better understanding.

$1! = 1$

$2! = 2 \times 1 = 2$

$3! = 3 \times 2 \times 1 = 6$

$4! = 4 \times 3 \times 2 \times 1 = 24$

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$

$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$

You can calculate factorial of any number with the multiplication process by decreasing the number by $1$ until you reach integer $1$.

Remember, the value of $0!$ is also equal to $1$.

$n! = n.(n-1).(n-2) \cdots 3.2.1$

(or)

$n! = 1.2.3 \cdots (n-2).(n-1).n$

The factorial of a number can also be expressed in product of sequence form algebraically.

$$n! = \prod_{\displaystyle x = 1}^{\displaystyle n} x$$

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Oct 22, 2024

Oct 17, 2024

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved