# Factorial (*n*!)

How to solve the factorial of a number (*n*!): formula, examples, and their solutions.

## Definition

*n*! means

multiply from *n* to 1.

So *n*! = *n*⋅(*n* - 1)⋅(*n* - 2) ... 3⋅2⋅1.

[ ! ] is read as [factorial].

## Example 1

5! is

multiplying from 5 to 1.

So 5! = 5⋅4⋅3⋅2⋅1.

5⋅4 = 20

3⋅2 = 6

20⋅6 = 120

So 120 is the answer.

## Example 2

7! is

multiplying from 7 to 1.

But, instead of writing 7⋅6⋅5⋅[4⋅3⋅2⋅1] / 4!,

write 7⋅6⋅5⋅[4!] / 4!.

By writing [4!],

you can solve this easier:

you can cancel this [4!] and the denomiantor's 4!.

(dark gray)

Cancel 4! (dark gray)

in both of the numerator and the denominator.

Then (given) = 7⋅6⋅5.

6⋅5 = 30

7⋅30 = 210

So 210 is the answer.

## Example 3: 1!

1! is 1.

This is because

1! means

multiply from 1 to 1.

## Example 4: 0!

0! is defined as 1.

So 0! = 1.