What is the highest common factor? The highest common factor (HCF) is the largest number shared between two numbers.

For example, the highest common factor of 28 and 12 is 4, as can be seen below:

  • Factors of 28: 1, 2, 4, 7, 14 and 28.
  • Factors of 12: 1, 2, 3, 4, 6 and 12.

Whilst 2 is also a factor of both numbers, the highest number they have in common is 4.

Finding the highest common factor of two numbers is also a helpful way for children to practice their times tables.

When do children learn about the highest common factor?

After learning about factors and prime numbers, teachers may introduce the term highest common factor to children in Year 6.

Children that have a good understanding of the highest common factor ( HCF) might be given more difficult questions to solve such as:

  • What is the highest common factor of 32, 48, and 96?

This is more complicated as it involves finding the HCF of three numbers, however finding the answer involves the same listing method:

  • Factors of 32: 1, 2, 4, 8, 16 and 32.
  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
  • Factors of 94: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

Although 94 and 48 both share the common factor 48, the HCF that all 3 numbers share is 16.

How might children struggle with the concept of the highest common factor?

Finding the HCF of any pair of numbers involves knowledge of the times tables, and this is a common obstacle for some children. Therefore, it is important to encourage children to practice using their times tables first, as confidence in this will be essential to their understanding of maths going forward.

Be aware that there is a strong temptation to leave times tables learning too early.

How to help children with the highest common factor?

The best way of improving a child’s understanding of the HCF is mainly through regular practice of progressively harder questions.

However, if children are struggling to grasp the concept of the HCF, it may be helpful to go back over the definition of a factor and make sure they are comfortable with this first. It is also helpful to continue using factor trees, as they help children visualise how a number breaks down into its factors. They can then use the diagram to identify the highest factor a pair of numbers has in common.

How does Learning Street help children with the highest common factor topic?

Highest common factors are dealt with towards the end of year six courses and there is frequent exposure in our 11 Plus, KS2 SATS and our Independent School entry preparation courses.

As we always do we will introduce the topic then extend and deepen understanding and then revise the topic. We ensure knowledge stays fresh with frequent exposure.

Of course, children won’t do well with highest common factor work unless they have very good times tables knowledge. Without rock solid times tables knowledge then there’s no amount of technique or practice that will help children advance beyond a basic level.

Fortunately, we do make sure all our children develop sound times tables skills and a secure knowledge of factors before moving onto the highest common factor topic.

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