NUMBER

Highest Common Factor

Learn the reliable method for highest common factor, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Common factors divide two or more numbers exactly; the HCF is the greatest one they share.

Picture itFind every factor pair
2 · THE METHOD

Follow these steps

  1. List the complete factor set for each number.
  2. Mark every factor shared by all the numbers.
  3. For the HCF, choose the greatest shared factor.
3 · WORKED EXAMPLES

See the method in action

Example 1

What is the highest common factor of 18 and 27?

  1. 18 = 9 × 2 and 27 = 9 × 3.
  2. Since 2 and 3 are distinct primes, the greatest common divisor is 9.
Answer: 9
Example 2

There are 48 red beads and 208 blue beads. They are divided into the greatest possible number of identical bags, with none left over. How many bags are made?

  1. 48 = 16 × 3 and 208 = 16 × 13.
  2. Since 3 and 13 are distinct primes, the greatest common divisor is 16.
  3. Each bag contains 3 red and 13 blue beads.
Answer: 16
4 · ELEVENSPRINT TIP

A useful shortcut

For the HCF, choose the greatest shared factor.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.