lesson
Factors and multiples solve different questions
1 · Learn
A factor divides a whole number exactly; a multiple is a whole-number product. A prime has exactly two positive factors and is greater than 1. The number 1 is not prime.
A highest common factor helps simplify a fraction. A lowest positive common multiple helps find a shared denominator. Do not swap the meanings because both involve multiplication facts.
2 · Worked example
18 and 30 share factors 1, 2, 3 and 6, so their highest common factor is 6. Multiples of 4 and 6 first meet at 12.
3 · Your turn
Find the highest common factor of 24 and 36, and the lowest positive common multiple of 8 and 12.
Check your answer
12 and 24 respectively.
4 · Apply your learning
Build factor pairs systematically and explain why 1, 21 and 29 have different classifications.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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