Factors Multiples HCF and LCM (Class 5)

What this worksheet covers

This is an eighteen-question practice worksheet on factors, multiples, hcf and lcm for Class 5, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on factors, multiples, hcf and lcm at Class 5 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done in the space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Factors Multiples HCF and LCM (Class 5) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. How many factors does 36 have?

   • A6
   • B8
   • C9correct
   • D12
   Solution: Pair up the factors: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
   The factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36 — that is 9 factors. (A perfect square always has an odd number of factors.)

2. 2. Three bells ring at intervals of 6, 8 and 12 minutes. If they ring together at 9:00 a.m., at what time will they next ring together?

   • A9:12 a.m.
   • B9:48 a.m.
   • C9:36 a.m.
   • D9:24 a.m.correct
   Solution: They ring together again after the LCM of 6, 8 and 12 minutes.
   6 = 2 × 3, 8 = 2³, 12 = 2² × 3.
   LCM = 2³ × 3 = 24 minutes, so they next ring together at 9:24 a.m.

3. 3. Consider the following statements.(i) Every prime number greater than 2 is odd.(ii) If a number is divisible by 4 and by 6, it must be divisible by 24.(iii) The HCF of two co-prime numbers is 1.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(i) and (iii) onlycorrect
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — any even number above 2 has 2 as a factor, so it cannot be prime. Statement (ii) is false; 4 and 6 share the factor 2, so the correct conclusion is divisibility by their LCM, 12. The number 12 itself is the counter-example. Statement (iii) is true by definition. Hence (i) and (iii).