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What are common factors?

Factors are numbers that divide exactly into a number. They are the multiplication 鈥渇acts鈥 of the number.

A common factor is a factor that is shared by two or more numbers.

The number 1 will be a common factor for every single number!

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Watch: Common factors

Watch this video for an introduction to common factors with Mr McPartlin.

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Watch: Find common factors with arrays

Watch this video for a quick guide on how to find common factors using arrays.

Find out how to work out the common factors of two numbers using eggs!

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Using an ordered method

To find common factors without using arrays, you can use a systematic approach (an ordered method).

Example 1

Bob the Baker has made a batch of 9 doughnuts and 15 custard tarts. He wants to divide them up and put them in boxes. One box is able to hold the same number of doughnuts as custard tarts. How many of each can one box hold?

Baker with empty box and trays of donuts and custard tarts

This question is asking you to find the common factor of 9 and 15.

Let鈥檚 find all the factors of 9 and 15 and see which factor they share!

Factors of 9:

1, 3 and 9

Factors of 15:

1, 3, 5 and 15

A tray of 9 donuts in a 3 by 3 grid and 15 tarts in a 5 by 3 grid

3 is the common factor.

So Bob the Baker鈥檚 boxes can hold 3 donuts or custard tarts!

Baker with 3 tarts and 3 donuts in a box
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Example 2

An illustration of a young girl thinking.

What are the common factors for 16 and 48?

First, write down all the factors for both numbers.

Start at the number 1 and work your way up to 12. Ask yourself whether that number is divisible into the other number. Sometimes you will find numbers have factors greater than 12.

Factors of 16:

1, 2, 4, 8 and 16

Factors of 48:

1, 2, 3, 4, 6, 8, 12 and 16

Now, see which factors both 16 and 48 have.

Common factors of 16 and 48 are 1, 2, 4, 8 and 16.

An illustration of a young girl thinking.
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What is a prime factor?

A prime factor is a factor which is also a prime number. Remember, 1 is not a prime number.

Example 3

Can you find all the common prime factors for 42 and 56?

First, find all the factors for 42 and 56.

Factors of 42:

1, 2, 3, 6, 7, 14 and 21.

Factors of 56:

1, 2, 4, 7, 8, 14 and 28.

Now you can see all of the common factors:

1, 2, 7 and 14.

But which of these numbers are prime numbers?

2 and 7, because they only have themselves and 1 as factors.

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Activity

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NEW! Play Guardians: Defenders of Mathematica - the winter update. game

It's Mathematica as you鈥檝e never seen it before, with all-new festive backgrounds and costumes. Available for a limited time only. Use your maths skills to save the day before it's too late!

NEW! Play Guardians: Defenders of Mathematica - the winter update
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More on Factors, multiples and primes

Find out more by working through a topic