JENECONKMaths Universe

Highest Common Factor (HCF)

Ages 9–13

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Highest Common Factor

The HCF (also called GCD — Greatest Common Divisor) of two or more numbers is the largest number that divides all of them evenly.

Your goals

  • ✓You can find the largest number that divides two or more numbers.
  • ✓You can use common factor, HCF correctly.
  • ✓You can confirm that your answer divides every starting number exactly.

Words to know

common factor:
A factor shared by each number being considered.
HCF:
The greatest positive common factor.

Examples

  • 1Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. HCF = 6
  • 2HCF(8, 20) = 4

Check these

  • • Do not choose a common factor without checking whether a larger one exists.
  • • Keep every number, symbol, label, and unit in its correct place.
  • • Show enough working to check how you reached your answer.

Helpful habits

  • • Read the whole question before choosing what to do.
  • • Show one clear step at a time and check each step.
  • • If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own highest common factor (hcf) example, solve it, and explain how you checked it.

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