Using Venn diagrams gives us a neat way to find common factors of a pair of numbers or common multiples of a pair of numbers

Common factors

To find the common factors of a pair of numbers, we find the set of factors of each number and then put them into a Venn diagram. The numbers in the intersection of the two sets are the common factors.

Worked Example

Draw a Venn diagram to show the factors of 6 and 9.

Exercise 1

Highest Common Factor

If we’ve drawn a Venn diagram with the common factors in the intersection, it’s easy to identify the HCF, this is just the biggest number amongst the common factors.

Worked Example

Use a Venn diagram to find the HCF of 18 and 24.

Exercise 2

Common Multiples

The approach with common multiples and to find the LCM or Lowest Common Multiple is very similar.

Worked Example

Use a Venn diagram to show which of the whole numbers from 1 to 25 are multiples of 3, which of them are multiples of 4 and which of them are both.

Use a Venn diagram to find the LCM of 4 and 6.

Exercise 3

Answers to all of the exercises above