✖️ Topics & explainers · 5 min read
Factors and multiples for Class 5: the two directions of the times table
A Class 5 explainer of factors, multiples, HCF and LCM in plain words, with worked examples and the factor-vs-multiple mix-up from SOF IMO.
Factors and multiples are the two directions of the times table. Factors of a number divide into it exactly, with nothing left over — the factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples go the other way: the multiples of 12 are 12, 24, 36 and so on, forever. Class 5 olympiad papers build some of their best puzzles on this one pair of ideas.
The idea in one minute
- A factor of a number divides it exactly: 8 is a factor of 24 because 24 ÷ 8 = 3 with no remainder.
- A multiple of a number is that number times something: 24 is a multiple of 8 (and of 1, 2, 3, 4, 6, 12 and 24).
- Factors are few and never bigger than the number; multiples are endless and never smaller than it.
- The LCM is the smallest number that is a multiple of both; the HCF is the biggest number that is a factor of both.
✏️ Warm-up: spot the factor
Which of these is a factor of 24?
- A5
- B7
- C8
- D9
Show the answerAnswer: 8
Answer: 8. Divide 24 by each option and look for no remainder. 24 ÷ 5 leaves 4, 24 ÷ 7 leaves 3, and 24 ÷ 9 leaves 6. Only 24 ÷ 8 = 3 exactly, so 8 is the factor.
✏️ Level up: the smallest common multiple
What is the LCM (lowest common multiple) of 4 and 6?
- A2
- B10
- C12
- D24
Show the answerAnswer: 12
Answer: 12. List multiples until they meet. Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18… The first number on both lists is 12. The traps: 2 is the HCF, not the LCM, and 24 is a common multiple but not the lowest one.
✏️ Olympiad twist: two conditions at once
A number is a multiple of both 3 and 5, and it lies between 20 and 40. What is the number?
- A25
- B30
- C35
- D45
Show the answerAnswer: 30
Answer: 30. A multiple of both 3 and 5 must be a multiple of 15: that gives 15, 30, 45… Only 30 lies between 20 and 40. The traps each fail one condition: 25 and 35 are multiples of 5 but not of 3, and 45 is a multiple of both but sits outside the range.
Factors and multiples anchor LittleMathematicians’s Class 5 Number Sense topic: levels move from spotting factors to LCM, HCF and two-condition puzzles like the last example as your child’s mastery grows. It is free during early access, and timed mocks then show how the topic behaves under exam pressure.
Practice this the fun way
Adaptive levels, exam-pattern mocks and progress you can see — free during early access.
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