Factorial exmaples. How to work out factorials easily (exclamations!)

To find a factorial of a number, multiply this number by all the numbers lower than itself until you reach 1. An exclamation sign is used to stand for factorial. If you like algebra, then try using the following formula:

n! = n × (n-1) × (n-2) ×(n-3) ... × 1

Example 1

Work out 4! (that is 4 factorial)

So start with 4, and multiply by all the number lower than 4 until you reach 1.

4×3×2×1 = 24

Example 2

Work out 7!

Like before, start with number 7, and multiply together all the numbers lower than 7  until you reach 1.

So we need to work out: 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

Example 3

Work out 3!

Again, start by 3 and multiply this by all the numbers smaller than 3 until you reach 1.

So 3! = 3×2×1 = 6

Example 4

Work out 10 facotrial.

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800.

Let’s take a look at a couple of harder examples:

Example 5

Work out 3! × 4!

First find 3 factorial and 4 factorial.

3! = 3×2×1 = 6

4! = 4×3×2×1 = 24

So all we need to do know is multiply these two numbers together:

6 × 24 = 144

Example 6

Work out 7! ÷ 4!

Again work out 7 factorial and 4 factorial.

7! = 5040 and 4! = 24

Now if we divide these numbers we get 210.

However, there is a quicker way to work out the last example

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

4! = 4×3×2×1

Now dividing these we get:

(7 × 6 × 5 × 4 × 3 × 2 × 1)/(4×3×2×1).

Now we cancel the 4’s, 3’s, 2’s and 1’s on the numerator and denominator of our fraction.

So we are left with 7 × 6 × 5. If we work this out this gives an answer of 210, the required answer.

Summary

To find a facotrial multiply the number by all the number lower than itself until you reach 1.

An exclamation mark can be used to represent factorial.

Look for the factorial button on your calculator to speed things up.