Why must 1 and the number itself always appear in a factor list?

Every whole number divides by 1 and by itself with no remainder, so both are always factors. Writing the pairs from 1 × the number keeps them in the list.

What fixed link joins the product, the H.C.F. and the L.C.M.?

H.C.F. × L.C.M. always equals the product of the two numbers, so 12 × 144 = 36 × 48 checks both answers at once.

Primary 4 Maths: Factors and Multiples — Practice Paper 2 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 2 works with another set of numbers: the factors of 45 and 36 are listed and counted, a prime check and a divisibility check follow, and short division gives the H.C.F. and L.C.M. of three pairs. The last three items are gift packs, a shared duty day and a list that lost 1.

Quick answer　10 questions, about 25 minutes. Items 01 to 03 cover the factors of 45, a prime check and a divisibility check; items 04 to 06 cover the nine factors of 36, the H.C.F. of 18 and 27 and the L.C.M. of 8 and 10; items 07 to 09 cover both values for one pair, gift packs (H.C.F.) and a shared duty day (L.C.M.); item 10 redoes the list missing 1 and 24.

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 45.
FoundationWhich of 17 and 21 is a prime number?
FoundationIs 60 divisible by 6? Show the division.
IntermediateList all the factors of 36 and say how many there are.
IntermediateFind the H.C.F. of 18 and 27.
IntermediateFind the L.C.M. of 8 and 10.
ChallengeFind the H.C.F. and the L.C.M. of 36 and 48.
Challenge45 pencils and 30 rulers are shared into identical gift packs. What is the greatest number of packs, and what goes into each one?
ChallengeOne student is on duty every 6 days and another every 9 days. They are both on duty today. After how many days will they next be on duty on the same day?
Error redoA student lists the factors of 24 as 2, 3, 4, 6, 8 and 12. Which two are missing, and how many factors does 24 have in all?

03　Answers and one-line notes

#	Answer	One-line note
1	1, 3, 5, 9, 15, 45 (6 factors)	Pair them: 1 × 45, 3 × 15, 5 × 9. Three pairs make 6 factors, and the check is that both ends of the list are present.
2	17	A prime has only 1 and itself as factors. 21 = 3 × 7 has four factors, while 17 divides only by 1 and 17.
3	Yes, 60 ÷ 6 = 10	Divisible means zero remainder: 6 × 10 = 60, so 6 is a factor of 60 and 60 is a multiple of 6.
4	1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors)	Pair them: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. The last pair repeats the same number, so 6 is written once, giving 9 factors in all.
5	9	Short division leaves 3 and 3 in the left column, and only that column is multiplied: 3 × 3 = 9. An H.C.F. never exceeds 18, the smaller number.
6	40	The left column holds 2 and the bottom row holds 4 and 5, so 2 × 4 × 5 = 40. An L.C.M. never falls below 10, the larger number.
7	H.C.F. = 12, L.C.M. = 144	Short division leaves 2, 2, 3 on the left, so 2 × 2 × 3 = 12 is the H.C.F.; the bottom row holds 3 and 4, giving 12 × 12 = 144. The check is H.C.F. × L.C.M. = 1728 = 36 × 48.
8	15 packs, each with 3 pencils and 2 rulers	The greatest number of identical packs is the H.C.F.: H.C.F.(45, 30) = 15, and 45 ÷ 15 = 3, 30 ÷ 15 = 2, so both are used up exactly.
9	18 days	The next shared day is the L.C.M.: L.C.M.(6, 9) = 18. The product 6 × 9 = 54 is also a common multiple, but not the smallest.
10	1 and 24 are missing; 8 factors in all	Writing the pairs from the outside in prevents omissions: 1 × 24, 2 × 12, 3 × 8, 4 × 6. Four pairs make 8 factors, and 1 and the number itself are always factors.

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.

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