Maths How To with Anita

# Factors of 18 and How to Find Them

What are the factors of 18? How can you find them?

This article will tell you everything you need to know about factors of 18, including factor pairs and prime factorization.

It also covers divisibility rules and how to identify positive and negative factors.

By the end of the article, you will know how to find the factors of any number. So whether you’re a student trying to ace a test or just curious about factors, read on!

## What are Factors?

Factors are the numbers that can be multiplied together to create the number in question.

For example 2 x 5 = 10 so 2 and 5 are called factors of 10.

## What are the Factors of 18?

The factors of 18 are 1, 2, 3, 6, 9, 18.

18 can be divided by these factors and the answer is a whole number.

## Factor pairs of 18

I like to think of factors in pairs because we multiply 2 numbers together to get 18.

1 x 18 = 18

2 x 9 = 18

3 x 6 = 18

Another way of finding factor pairs is to draw a factor rainbow.

Then 2 and 9.

Followed by 3 and 6.

The only numbers left between 3 & 6 are 4 and 5 and they aren’t factors of 18. This is how you know you’ve found all the factors.

## Prime Factors

Prime numbers have exactly 2 factors. 1 and itself.

For example 2, 3, 5, 7, 11 can only be divided by 1 and themselves.

So they are called prime numbers.

If a number has more than 2 factors it is called a composite number.

For example 1 x 4 = 4 and also 2 x 2 = 4 so the factors of 4 are 1, 2 & 4.

Since this is more than 2 factors, 4 is a composite number.

Prime factors are factors of a number that are also prime numbers.

## Prime factors of 18

To find the prime factors of 18 draw a factor tree. Each branch of the factor tree is 2 numbers that multiply to give the number above.

I like to circle the prime factors so I know the branches stop on them.

Once you have your factor tree, you can see the prime factors are circled in red.

So the prime factorization of 18 is

18 = 2 x 3 x 3

or in index notation

## Divisibility tests to find the factors of 18

The divisibility tests are shortcuts to help you quickly find factors of a number.

Let’s go through each divisibility test

• 1 is a factor of every number so there is no divisibility test for 1.
• If the last digit is an even number (0,2,4,6,8) then the number is divisible by 2 meaning 2 is a factor of the number. Since the last digits of 18 is 8 which is an even number it is divisible by 2.
• If the sum of the digits is divisible by 3 then the number is divisible by 3. For example in 18, 1 + 8 = 9 which is divisible by 3 since 3 x 3 = 9. So therefore 18 is divisible by 3, meaning 3 is a factor of 18.
• If the last 2 digits of a number is divisible by 4, then the number is divisible by 4. For example the last 2 digits of 56712 are 12 and 4 is a factor of 12 since 4 x 3 = 12, then 4 is a factor of 56712. The last 2 digits of 18 are 18 which is not divisible by 4 since the multiples of 4 are 4,8,12,16,20.
• If the last digit is 5 or 0, then the number is divisible by 5. For example 73845 ends in 5 so it is divisible by 5. 18 doesn’t end in 5 or 0 so 5 is not a factor of 18.
• If both 2 and 3 are factors of a number then 6 is also a factor of the number. Since 2 and 3 are both factors of 18, 6 is also a factor of 18.
• There is no divisibility test for 7.
• If both 2 and 4 are factors of a number then 8 is also a factor of the number. Since 4 is not a factor of 18, 8 is also not a factor.
• If the sum of the digits is divisible by 9 then the number is divisible by 9. So for 18, 1 + 8 = 9 which is divisible by 9 so 9 is a factor of 18.
• If the last digit is a 0, then 10 is a factor of the number. 10 is not a factor of 18.

## Negative factors of 18

The negative factors of 18 are simply -1, -2, -3, -6, -9, -18.

If you are thinking of factor pairs, then both numbers need to be negative or both numbers need to be positive.

For example -2 x -9 = 18

## Final Thoughts on Factors of 18

Factorizing is an important skill that will help you with other math topics down the road, like algebra. It’s a process of breaking down numbers into their factors- and once you understand how to do it, it becomes much easier to solve equations.

Don’t worry if factoring seems difficult at first- with a little practice and mastering your times tables you’ll be able to get the answer every time.

For further reading have a look at the 18 times tables.