What is the highest common factor?

What is the highest common factor?
We explain what the highest common factor is and give examples of how the concept might be taught to your primary school child.

What is the highest common factor?

The highest common factor of two numbers is the largest whole number which is a factor of both. Teachers may introduce this concept to more able Year 6 children.

A factor is one of two or more numbers that divides a given number without a remainder.

Finding the highest common factor

To work out the highest common factor of two numbers, start by listing all the factors then compare the lists to find the largest number they have in common. For example:

What is the highest common factor of 16 and 48?

Factors of 16 are 1, 2, 4, 8 and 16.

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

So the highest common factor of 16 and 48 is 16.

A more difficult challenge may be to ask for the highest common factor of a group of three or four numbers.

For example:

What is the highest common factor of 21, 36 and 42?

Factors of 21 are 1, 3, 7 and 21.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

So the highest common factor of these three numbers is 3.

Finding the highest common factor of two numbers is an excellent way of getting children to practise their times tables and division facts. It also helps them to familiarise themselves with the term 'factors'.

A good challenge would be to give children puzzles where the factor rather than the original numbers are given, for example:

Two numbers have a highest common factor of 7. What could the two numbers be?

This way, children need to think carefully about what the numbers could be, then whittle the answer down to two numbers by a process of elimination.

(The answer to the above could be 14 and 49, but there may be other answers.)