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Find the Highest Common Factor

In this worksheet, students will find the Highest Common Factors (HCF) of number pairs by creating lists and finding the highest option which appears in both lists.

'Find the Highest Common Factor' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Whole Number Theory

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Finding the Highest Common Factor (HCF) is an important topic in maths that is useful in a number of skills, including fractions, mental maths, problem solving and many more.

Sometimes the HCF is referred to as the Greatest Common Factor (GCF) too - these meanings are identical. 

 

In this activity, we will learn about how to find the HCF using lists.

 

What does HCF mean?

 

A factor is a number that you can divide a target by without leaving a remainder. 

Common means that it appears more than once.

So the HCF is just the highest number that appears in the factor list for two (or more) numbers.

 

 

e.g. Find the HCF of 10 and 25.

 

The first step for these questions is to write out a list of all the factors:

10: 1,2,5,10

25: 1, 5, 25

 

From this, we can see that the largest number that appears in both lists is 5.

So the HCF of 10 and 25 is 5.

 

 

 

In this activity, you will find the HCFs of number pairs by creating lists and finding the highest option which appears in both lists. 

You may want to have a pen and paper handy so that you can write out your lists before selecting your answers. 

Complete the acronym to summarise what HCF means. 

What is the HCF of 6 and 9?

Which option in the list is the HCF of 4 and 8?

1

2

4

8

What is the Greatest Common Factor of 12 and 25?

Which of the options in the list are common factors of 20 and 30?

1

2

5

10

20

30

Match each number pair below with its Highest Common Factor.

Column A

Column B

5 and 7
5
5 and 10
1
13 and 39
13

True or False?

 

The HCF of two prime numbers must be 1.

True

False

What is the HCF of 1 and any other number?

What is the HCF of 28 and 35?

Complete the sentence below to summarise how to find HCFs. 

  • Question 1

Complete the acronym to summarise what HCF means. 

CORRECT ANSWER
EDDIE SAYS
You'll see this written most commonly as HCF - mathematicians are lazy and don't like writing out the full wording every time! HCF stands for:

Highest, Common, Factor

  • Question 2

What is the HCF of 6 and 9?

CORRECT ANSWER
3
EDDIE SAYS
Remember that the first thing to do here is to write out two lists of the factors: 3: 1, 3 9: 1, 3, 9 Can you identify the highest number which appears in both lists? That's right, it's 3.
  • Question 3

Which option in the list is the HCF of 4 and 8?

CORRECT ANSWER
4
EDDIE SAYS
Your lists should read: 4: 1, 2, 4 8: 1, 2, 4, 8 Can you spot the highest number which appears in both lists? The common mistake here is to miss that 4 is a factor of 4. If you remember to write your lists out fully, you'll never fall into this trap.
  • Question 4

What is the Greatest Common Factor of 12 and 25?

CORRECT ANSWER
1
EDDIE SAYS
Don't let the word "Greatest" trip you up - it just means the same as "Highest". Let's list our factors here. 12: 1, 2, 3, 4, 6, 12 25: 1, 5, 25 It's an extremely common mistake to say that these numbers don't have a common factor. Don't forget that 1 is a factor of everything and that is our only option here!
  • Question 5

Which of the options in the list are common factors of 20 and 30?

CORRECT ANSWER
1
2
5
10
EDDIE SAYS
Be really careful when you read questions. This one doesn't ask for the highest common factor; it simply asks for the common factors. So you are looking for all the factors which appear in the factor lists for both 20 and 30: 20: 1, 2, 4, 5, 10, 20 30: 1, 2, 3, 5, 6, 10, 15, 30 The common factors between both lists are: 1, 2, 5 and 10
  • Question 6

Match each number pair below with its Highest Common Factor.

CORRECT ANSWER

Column A

Column B

5 and 7
1
5 and 10
5
13 and 39
13
EDDIE SAYS
You could write out all the lists here to compare, and that's no problem if you did. There are a couple of little tricks which will help you with questions like these though. 5 and 7 are both prime numbers, so what must their highest common factor be? It has to be 1 as prime numbers only have factors of themselves and 1. 10 is a multiple of 5, so the HCF here must be 5. Why must 13 be the HCF of 13 and 39? Because it is the highest option out of the lower pairings. Great work if you spotted any of those shortcuts to the answers here!
  • Question 7

True or False?

 

The HCF of two prime numbers must be 1.

CORRECT ANSWER
True
EDDIE SAYS
A prime number only has two factors: 1 and itself. So if two prime numbers appear in a pairing, the only factor they will have in common is 1. The only way the HCF could be more than 1 is if the numbers are exactly the same.
  • Question 8

What is the HCF of 1 and any other number?

CORRECT ANSWER
1
EDDIE SAYS
The number 1 only has 1 factor. So whenever it appears in a pairing, the highest common factor will always be 1, no matter what the other number is. This is a useful rule to remember and use when it is required.
  • Question 9

What is the HCF of 28 and 35?

CORRECT ANSWER
7
EDDIE SAYS
Let's follow our process again. Write out the list of factors for both numbers: 28: 1, 2, 4, 7, 14, 28 25: 1, 5, 7, 35 7 is the highest number which appears in both lists so this is the HCF.
  • Question 10

Complete the sentence below to summarise how to find HCFs. 

CORRECT ANSWER
EDDIE SAYS
This is the key rule to take from this activity: Write out the two lists, compare them, then pick out the highest, common number. Job done! Why not revise factors and multiples if you found any of these questions challenging?
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