SM4.3 Factors, multiples and divisibility
You can test divisibility by the small numbers at sight, find HCF and LCM quickly, and use them on the remainder and together-again questions examinations ask.
Topics shown in module order.
This topic is the Real numbers chapter turned into speed: the divisibility tests for 2 through 11, prime factorisation done briskly, and HCF and LCM chosen correctly for the question at hand. The classic examination forms are bells that ring together, tiles that fit a floor exactly, and the largest number that divides two others leaving given remainders, and each is HCF or LCM wearing a story.
Work through these
Learn the divisibility tests through 11 and apply them to a list of large numbers at sight
The tests turn division into a glance, and they compound: divisibility by 6 is the tests for 2 and 3 together. At sight is the standard to hold, because that is the speed at which they save time.
Decide for a set of word problems whether each wants HCF or LCM, before computing either
Fitting exactly inside points to HCF and coinciding again points to LCM, and the deciding is the examined skill. Sorting first and computing second practises the decision separately from the arithmetic.
Solve two bells-ringing-together and two remainder questions in full
These are the two costumes the topic wears in papers year after year. The remainder variant needs one extra thought, subtracting the remainders before taking the HCF, and doing it twice makes the thought stick.
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Links last checked 7 Sept 2026.
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