number · Year 7 · Suggested learning sequence

Highest common factor and lowest common multiple

The highest common factor (HCF) of two numbers is the biggest number that divides both. List the factors of each and find the largest on both lists. The lowest common multiple (LCM) is the smallest number both divide into. List multiples of the larger number until you reach one the smaller number also divides. HCF answers 'largest equal groups' questions; LCM answers 'when will they happen together again' questions.

Sample questions

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The factors of 32 are 1, 2, 4, 8, 16, 32. What is the highest common factor of 40 and 32?

  1. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Factors of 32: 1, 2, 4, 8, 16, 32.
  2. The common factors are 1, 2, 4, 8.
  3. The highest common factor is 8.

Answer: 8

The factors of 25 are 1, 5, 25. The factors of 35 are 1, 5, 7, 35. What is the highest common factor of 25 and 35?

  1. Factors of 25: 1, 5, 25. Factors of 35: 1, 5, 7, 35.
  2. The common factors are 1, 5.
  3. The highest common factor is 5.

Answer: 5

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. What is the highest common factor of 36 and 30?

  1. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
  2. The common factors are 1, 2, 3, 6.
  3. The highest common factor is 6.

Answer: 6

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