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🎯 Topics & explainers · 7 min read

Decimals, factors & multiples for the Class 5 olympiad

The Class 5 Number Sense pair in the SOF IMO: comparing decimals, factors and multiples, the “longer decimal is bigger” trap, and worked examples.

By Class 5, the IMO’s Number Sense questions grow two new branches: decimals, and factors & multiples. Both look like plain school topics — until the olympiad twist appears. Decimals get compared where the “longer” number is actually smaller, and factor questions flip into which option is NOT a factor, or which number divides two others but not a third.

These two branches also feed directly into everyday-math questions about money and measurement, and into the Achievers Section, where a single factors question can carry more marks than a regular one. Fluency here is one of the highest-value investments a Class 5 child can make.

What your child needs to know

  • Decimal place value: tenths, hundredths, thousandths — and that 0.5, 0.50 and 0.500 are the same number.
  • Comparing and ordering decimals by lining up the decimal points, not by counting digits.
  • Converting between simple fractions and decimals: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75.
  • Finding all factors of a number, and listing multiples.
  • Common factors and common multiples of two numbers.
  • Divisibility clues: even numbers, numbers ending in 0 or 5, and digit sums for 3 and 9.

The traps olympiad setters use

  • The longer-is-bigger trap: 0.505 has more digits than 0.55, but 0.55 is bigger. Pad to the same length — 0.550 vs 0.505 — and compare.
  • Factors vs multiples swapped mid-question: 6 is a factor of 24; 24 is a multiple of 6. Setters count on children blurring the two words.
  • The word NOT: “which is NOT a factor of 48” punishes a child who stops at the first factor they recognise.
  • Forgetting the edges: 1 is a factor of every number, and every number is a factor and a multiple of itself.

✏️ Try it: comparing decimals (Class 5 level)

Which of these numbers is the greatest?

  1. A0.5
  2. B0.45
  3. C0.505
  4. D0.055
Show the answer

Answer: 0.505. Pad every number to three decimal places: 0.500, 0.450, 0.505, 0.055. Now compare like whole numbers of thousandths: 505 beats 500, 450 and 55, so 0.505 is greatest. A child who counts digits picks 0.055 (“longest”) or stops at 0.5 (“5 tenths sounds big”) — the padding habit defeats both traps.

✏️ Try it: common factors (Class 5 level)

Which number is a factor of both 24 and 36, but NOT a factor of 20?

  1. A4
  2. B5
  3. C6
  4. D8
Show the answer

Answer: 6. Test each option. 4 divides 24, 36 and also 20 — ruled out by the “NOT”. 5 does not divide 24 at all. 8 divides 24 but not 36 (36 ÷ 8 leaves a remainder). 6 works: 24 ÷ 6 = 4 and 36 ÷ 6 = 6, while 20 ÷ 6 leaves a remainder. Notice how the question really tests careful checking of all three conditions, not just knowing what a factor is.

In LittleMathematicians, decimals and factors & multiples are separate Class 5 game levels, each tracking its own mastery — so a child strong in decimals but shaky on common factors gets exactly the practice that closes the gap. It is free during early access, and timed mocks then mix both into the full exam pattern.

Practice this the fun way

Adaptive levels, exam-pattern mocks and progress you can see — free during early access.

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Keep reading

Factors and multiples for Class 5: the two directions of the times tableA 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.5 min read →Class 5 IMO preparation: decimals, factors and a longer paperPreparing a Class 5 child for the SOF IMO: decimals, factors and multiples, fraction operations — and why the paper gets longer from this class.7 min read →Fractions for the Math Olympiad (Classes 4–5)Fractions in the SOF IMO for Classes 4–5: equivalent fractions, comparing, the “bigger denominator” trap, and two worked olympiad-style examples.6 min read →