Factorial (n!)

Factorial (n!)

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

Definition

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

n! means
multiply from n to 1.

So n! = n⋅(n - 1)⋅(n - 2) ... 3⋅2⋅1.

[ ! ] is read as [factorial].

Example 1

Find the value of the given number. 5!

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

Find the value of the given number. 7!/4!

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!

Find the value of the given number. 1!

1! is 1.

This is because
1! means
multiply from 1 to 1.

Example 4: 0!

Find the value of the given number. 0!

0! is defined as 1.

So 0! = 1.