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Common factors and multiples – practice for Years 6–7

Sample questions on Common factors and multiples with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 6–7
Curriculum area
Number and algebra

Question types: Highest common factor and lowest common multiple

Rule: Common factors and multiples

Write both numbers as products of prime numbers.

HCF(a, b): multiply the primes they share. LCM(a, b): take each prime as many times as it appears at most.

Example: 24 = 2 × 2 × 2 × 3, 30 = 2 × 3 × 5: HCF = 2 × 3 = 6, LCM = 2 × 2 × 2 × 3 × 5 = 120

Watch out: Which one: equal pieces as long as possible with nothing left over → HCF; when things meet again → LCM.

Sample questions

  1. Question 1 Easy

    Find the highest common factor of 24 and 30: HCF(24, 30) = ?

    Show the solution
    Answer: 6

    How it works: 24 = 2 × 2 × 2 × 3, 30 = 2 × 3 × 5; HCF(24, 30) = 2 × 3 = 6

  2. Question 2 Normal

    Find the highest common factor of 54 and 63: HCF(54, 63) = ?

    Show the solution
    Answer: 9

    How it works: 54 = 2 × 3 × 3 × 3, 63 = 3 × 3 × 7; HCF(54, 63) = 3 × 3 = 9

  3. Question 3 Hard

    Two ribbons, 40 cm and 70 cm long, are cut into pieces of equal length with nothing left over, as long as possible. How long is each piece?

    Show the solution
    Answer: 10 cm

    How it works: 40 = 2 × 2 × 2 × 5, 70 = 2 × 5 × 7; HCF(40, 70) = 10 cm

Related topics

All Maths topics

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