Question P6 Factors and multiples
Today’s problem — free all day, every step. Every day has one.
Two numbers are each less than 40 and add up to 60. Each of them has exactly 6 factors. What are the two numbers?
Answer
28 and 32.
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.
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.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.