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Primary 4 Maths: Factors and Multiples — Practice Paper 3 (10 Questions)
Primary 4 Maths: Factors and Multiples — Practice Paper 3 (10 Questions)
Paper 3 adds multiples written in order and a number with many factors, then asks for both the H.C.F. and the L.C.M. of one pair. The last three items are fruit baskets, two bus routes meeting again, and the frequent slip of handing in the L.C.M. as the H.C.F.
Quick answer 10 questions, about 25 minutes. Items 01 to 03 cover the factors of 28, the first multiples of 9 and a prime check; items 04 to 06 cover the twelve factors of 60, the H.C.F. of 24 and 36 and the L.C.M. of 12 and 18; items 07 to 09 cover both values for 24 and 40, fruit baskets (H.C.F.) and two buses (L.C.M.); item 10 redoes the H.C.F. given as the L.C.M.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | 25 minutes |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: Primary 4 Maths: Factors and Multiples (H.C.F. and L.C.M.) — Tutor Lesson Plan |
| Level | Primary 4 |
02 Questions (10 items)
- FoundationList all the factors of 28.
- FoundationWrite the first five multiples of 9, smallest first.
- FoundationIs 51 a prime number? Give a reason.
- IntermediateList all the factors of 60 and say how many there are.
- IntermediateFind the H.C.F. of 24 and 36.
- IntermediateFind the L.C.M. of 12 and 18.
- ChallengeFind the H.C.F. and the L.C.M. of 24 and 40.
- Challenge42 apples and 56 oranges are shared into identical baskets with the same contents. What is the greatest number of baskets, and what goes into each?
- ChallengeOne bus leaves every 12 minutes and another every 18 minutes. They leave together now. After how many minutes will they next leave together?
- Error redoA student answers H.C.F.(12, 18) = 36. What went wrong, and what are the H.C.F. and the L.C.M.?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1, 2, 4, 7, 14, 28 (6 factors) | Pair them: 1 × 28, 2 × 14, 4 × 7. Three pairs make 6 factors, and working from the outside in keeps the list complete. |
| 2 | 9, 18, 27, 36, 45 | Multiples come from multiplying: 9 × 1 up to 9 × 5. Every one divides by 9 with no remainder. |
| 3 | No, 51 = 3 × 17 | A prime has only 1 and itself as factors, but 51 ÷ 3 = 17, so it has four factors and is composite. |
| 4 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 (12 factors) | Pair them: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10. Six pairs make 12 factors, and no number repeats inside the list. |
| 5 | 12 | Short division leaves 2, 2, 3 in the left column and only that column is multiplied: 2 × 2 × 3 = 12, which divides both 24 and 36 exactly. |
| 6 | 36 | The left column holds 2 and 3 and the bottom row holds 2 and 3, so 2 × 3 × 2 × 3 = 36, which divides by both 12 and 18. |
| 7 | H.C.F. = 8, L.C.M. = 120 | Short division leaves 2, 2, 2 on the left, so the H.C.F. is 8; the bottom row holds 3 and 5, giving 8 × 15 = 120. The check is 8 × 120 = 960 = 24 × 40. |
| 8 | 14 baskets, each with 3 apples and 4 oranges | The greatest number of identical baskets is the H.C.F.: H.C.F.(42, 56) = 14, and 42 ÷ 14 = 3, 56 ÷ 14 = 4, so nothing is left over. |
| 9 | 36 minutes | The next shared departure is the L.C.M.: L.C.M.(12, 18) = 36 minutes. The product 12 × 18 = 216 is a common multiple, but not the smallest one. |
| 10 | 36 is the L.C.M.; H.C.F. = 6 and L.C.M. = 36 | The H.C.F. is the left column only, 6, and it can never exceed 12; multiplying by the bottom row gives the L.C.M., 36. The check is 6 × 36 = 216 = 12 × 18. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
