What is factorial?

A factorial is a number defined as follows for a positive integer \(n\).

\[ n!=n\left(n-1\right)\left(n-2\right)\cdots3\cdot2\cdot1 \]

For example, the factorial of 5 can be calculated as follows

\[ 5!=5\cdot4\cdot3\cdot2\cdot1=120 \]

It is common to define the factorial of 0 as 1.

\[ 0!=1 \]

Example

Example 1

Calculate \(3!\).

Solution

\[ 3!=3\cdot2\cdot1=6 \]

Exapmple 2

Calculate \(4!\).

Solution

\[ 4!=4\cdot3\cdot2\cdot1=24 \]