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PSLE 2024 — Two numbers six factors
Two numbers are each less than 40 and add up to 60. Each of them has exactly 6 factors. What are the two numbers?
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28 and 32.
The pattern behind it: Factors and multiples
The answer comes from how the numbers divide, not from a bar model.
In this one. The factor count comes from the powers in the prime factorisation — add one to each power and multiply — so 6 = 3 × 2 or 6 = 6 × 1 means the number can only be p² × q or p⁵, which turns a hunt over 39 numbers into a five-item list.
How to spot it
Words like 'as many teams as possible', 'equally divided with none left over', or 'has exactly this many factors' appear, without any ratio or fraction in sight.
Common mistake
Children reach for the lowest common multiple when the question needs the highest common factor, or try to list every factor of a number by hand instead of building it from its prime factors.
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.