NUMBER

Factors

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

1 · WHAT YOU NEED TO KNOW

The idea

Factors divide a number exactly with no remainder.

Picture itFind every factor pair
2 · THE METHOD

Follow these steps

  1. Test divisors systematically up to the square root.
  2. Record both numbers in each factor pair.
  3. Check that every factor pair multiplies to make the original number.
3 · WORKED EXAMPLES

See the method in action

Example 1

Which number is a factor of 273?

  1. 13 × 21 = 273.
  2. Therefore 13 divides 273 exactly, and 273 is a multiple of 13.
  3. Every other option leaves a remainder.
Answer: 13
Example 2

252 counters are divided into equal groups with none left over. Which number could be the size of each group?

  1. 21 × 12 = 252.
  2. Therefore 21 divides 252 exactly, and 252 is a multiple of 21.
  3. Every other option leaves a remainder.
Answer: 21
4 · ELEVENSPRINT TIP

A useful shortcut

Check that every factor pair multiplies to make the original number.

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.