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Highest Common Factor: GCSE Maths Definition

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Published

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2 minutes

Contents

  1. 1. What is the highest common factor?
  2. 2. How can I find the highest common factor?
  3. 3. What is the highest common factor used for?
  4. 4. Highest common factor revision resources to ace your exams

What is the highest common factor?

In GCSE Maths, the highest common factor (HCF) is the largest factor that is shared by two or more numbers.

For example, the highest common factor of the numbers 60 and 18 is 6.

How can I find the highest common factor?

There is more than one way to find the highest common factor of two numbers.

Listing factors

You can find common factors of two numbers by listing out all of the factors in each number and identifying which factors are common to both. The greatest of these values will be the highest common factor.

For example:

bold 28 colon space 1 comma space 2 comma space circle enclose 4 comma space 7 comma space 14 comma space 28 space space space space space space space space space space space space space bold space bold space bold 36 colon space 1 comma space 2 comma space 3 comma space circle enclose 4 comma space 6 comma space 9 comma space 12 comma space 18 comma space 36

The common factors of the numbers 28 and 36 are 1, 2 and 4. Therefore the HCF is 4.

Prime factor decomposition

You can also use prime factor decomposition to find the HCF of two numbers.

Break down the numbers into their prime factors and multiply together all prime factors that are common to both numbers. You may use the product of primes, a factor tree or a Venn diagram to do this.

For example:

Venn diagram showing the prime factors of the numbers 42 and 90. In the region of the diagram for 42 only, the only prime factor is 7. In the region of the diagram for 90 only, the prime factors are 3 and 5. In the region for both 42 and 90 are the prime factors 2 and 3.

The HCF of 42 and 90 is 2 cross times 3 equals 6

What is the highest common factor used for?

The highest common factor can be useful in a number of different situations to share out a quantity into its biggest groupings, e.g.

  • Cutting up two ribbons of different lengths to smaller pieces of equal size

  • Choosing the correct sizes of packing boxes so you can pack two orders of different quantities of a particular item without leaving any empty space in the boxes

Highest common factor revision resources to ace your exams

The highest common factor is covered in our revision notes on HCF & LCM from GCSE Maths. You can also have a go at our related exam questions and flashcards to test your understanding. Don’t forget to check out the past papers for more general exam revision.

Explore our GCSE Maths Revision Resources

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Author
Reviewer
Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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