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studyNumber & Proportion
FoundationMaths revision

Prime Numbers, HCF, and LCM

Use prime structure to analyse factors, multiples, divisibility and repeating cycles.

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Focus points
✓Write integers as products of primes.
✓Use prime powers to find HCF and LCM.
✓Recognise when an LCM or HCF model fits a problem.
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The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · prime factorisation
Write 756 as a product of prime factors in index form.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · HCF
Find the HCF of 84 and 126 using prime factors.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · LCM
Find the LCM of 72 and 90.
Question 4ApplicationCore
Original practice · Free Online Revision
Skill · LCM application
Two warning lights flash every 18 s and 30 s. They flash together now. After how many seconds will they next flash together?
Question 5ApplicationCore
Original practice · Free Online Revision
Skill · HCF application
A teacher has 96 red counters and 144 blue counters. She wants identical packs with no counters left over. What is the greatest possible number of packs?
Question 6ReasoningCore
Original practice · Free Online Revision
Skill · primality reasoning
Without listing all factors, decide whether 391 is prime.
Question 7ReasoningStretch
Original practice · Free Online Revision
Skill · prime-power HCF/LCM
Given a = 2³×3²×5 and b = 2×3⁴×7, find HCF(a,b) and LCM(a,b).
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · HCF-LCM identity
The HCF of two integers is 12 and their LCM is 420. One integer is 60. Find the other integer.