Question 1: Find the HCF of 12 and 18.

Answer: 6

Question 2: Calculate the HCF of 8 and 20.

Answer: 4

Question 3: Determine the HCF of 15 and 25.

Answer: 5

Question 4: Find the HCF of 9 and 14.

Answer: 1

Question 1: Two numbers have an HCF of 4. One number is 24. What could the other number be? Justify your answer.

Answer: Any multiple of 4 that divides 24, such as 8, 12, or 20, but not 16.

Question 2: A student claims the HCF of 30 and 45 is 15 because both end with 5. Is this correct? Explain your reasoning.

Answer: No, the HCF is 15 because 15 divides both 30 and 45. The fact they end with 5 is a coincidence, not a rule for HCF.

Question 1: A factory produces small boxes in packs of 12 and 18. What is the largest size of each pack that can be evenly divided into both types? Explain your method.

Answer: The largest size is the HCF of 12 and 18, which is 6, so packs of 6 units.

Question 1: Find two numbers less than 50 that have an HCF of 4 but are not multiples of 8. Show your working.

Answer: Examples include 20 and 36, as HCF is 4; 20 is multiple of 4 but not 8, 36 is multiple of 4.

Question 2: Prove that the HCF of two numbers is always less than or equal to the smaller number. Provide examples.

Answer: The HCF divides both numbers, so it cannot be larger than the smaller number. For example, HCF of 15 and 20 is 5, which is less than or equal to 15.

Question 1: Student's mistake: The HCF of 16 and 24 is 8 because 8 is a common multiple. Correct the mistake and find the actual HCF.

Answer: The mistake is confusing multiple with divisor. The HCF is 8 because 8 divides both 16 and 24.

Question 2: Student's claim: The HCF of 14 and 35 is 7 because 7 is a prime number. Is this reasoning correct? Explain.

Answer: Yes, 7 divides both 14 and 35, so the HCF is 7. The fact that 7 is prime is unrelated to the HCF calculation.