The pattern
Factors and multiples
The answer comes from how the numbers divide, not from a bar model.
Some questions never touch a bar or a ratio; the answer sits in how a number divides. Sharing two groups into equal teams with nothing left over calls for the highest common factor. Finding numbers with a set number of factors means breaking each one into its prime building blocks first.
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.
3 worked solutions
Standard
Challenging
- 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?
- PSLE 2025 — Sam and ava Sam and Ava have the same amount of money. The amount each had was less than $40. Ava bought some pillows at $8 each and had $3 le…
All the problem patterns → · the revision list
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.