Question 1: Find the HCF of 12 and 18.

Answer: 6

Question 2: Calculate the HCF of 8, 12, and 20.

Answer: 4

Question 3: Determine the highest number that divides 15 and 25 without leaving a remainder.

Answer: 5

Question 4: Construct a pair of numbers between 10 and 20 that have an HCF of 4. Show your reasoning.

Answer: Any two numbers such as 12 and 16 since HCF(12,16)=4

Question 5: Find the HCF of 9 and 14. Explain why it is what you calculated.

Answer: 1 because 9 and 14 share no common factors other than 1

Question 6: A bakery packages 24 cupcakes and 36 cupcakes. What is the largest number of identical boxes they can use so that each box has the same number of cupcakes? Show your working.

Answer: 12

Question 7: Calculate the HCF of 21 and 28 using prime factorization.

Answer: 7

Question 8: Find two numbers less than 20 with an HCF of 3. Provide the numbers and reasoning.

Answer: Examples include 12 and 15 since HCF(12,15)=3

Question 9: What is the HCF of 16 and 22? Show your working.

Answer: 2

Question 10: Identify the common factors of 18 and 24, then determine the HCF.

Answer: Factors of 18: 1, 2, 3, 6, 9, 18; Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24; HCF=6

Question 11: A student incorrectly concludes that the HCF of 14 and 21 is 7 because both are divisible by 7. Is this reasoning correct? Justify your answer.

Answer: Yes, because 7 divides both numbers exactly, and it is their highest common factor.