# Identify common factors, common multiples and prime numbers

## Home learning focus

Learn how to identify common factors, common multiples and prime numbers

This includes:

• two videos
• two worksheets

# Learn

### What is a common factor

In this video from BBC Bitesize find out how to work out the common factors of two numbers using eggs!

A factor is a number that divides into another number exactly. To find the common factors of two numbers, you first need to list all the factors of each one and then compare them.

If a factor appears in both lists then it is a common factor.

For example, the factors of 8 are:

1, 2, 4 and 8

The factors of 12 are:

1, 2, 3, 4, 6 and 12

Therefore, the common factors of 8 and 12 are:

1, 2, and 4

### What is a common multiple

The multiples of a number are all the numbers that it will divide into.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66

12, 24, and 36 are multiples of both 4 and 6 and are known as the common multiples of 4 and 6.

### Identifying prime numbers

• A prime number will only have two factors.

• A prime number will only be divisible by 1 and by itself.

One way to test if a number is prime, is to use some playing cards. The number of cards we need depends on what number we are testing.

Firstly, arrange the cards so that they form a single column. Using the same amount of cards try to form a perfect rectangle with two columns of cards. If you are able to form a perfect rectangle that does not have a height of one, then your number is not prime.

This is demonstrated in the below KS3 Maths video.

### Which of the numbers, 1 to 12, are prime?

• 1 is not a prime number as it only has one factor - itself.
• 2 is prime as it forms a rectangle that is 1 card by 2. So 2 only has two factors.
• 3 is prime as this forms a rectangle that is 1 card by 3. It has only two factors.
• 4 is the next number. We can see that 4 is not prime. This is because you can form a 2 x 2 rectangle, which has 2 columns.
• 5 is prime as it forms a rectangle that is 1 card by 5. It only has two factors.
• 6 is not prime as it can form a rectangle that is 3 x 2.

Can you work out the remaining primes between 7 and 12?

# Practise

## Activity 1

Multiples and factors worksheet

Can you complete the multiples and factors challenges on this worksheet from Collins?