Question 1: Find the HCF of 48 and 180.

Answer: 12

Question 2: Simplify the ratio 36:48 using the HCF method.

Answer: 3:4

Question 3: Calculate the HCF of 81, 54, and 27.

Answer: 27

Question 4: A recipe requires 24g of sugar and 36g of flour. Use the HCF method to simplify the ratio of sugar to flour.

Answer: 2:3

Question 5: The lengths of two sides of a rectangle are in the ratio 15:20. If the HCF of these lengths is 5, what are the lengths?

Answer: 15 and 20 (or scaled multiples of 3 and 4, e.g., 15 and 20)

Question 6: Construct a triangle with side lengths in the ratio 10:15:20. Use the HCF method to find the simplest form of these ratios.

Answer: 2:3:4

Question 7: A class has 24 boys and 36 girls. Use the HCF method to determine the maximum number of balanced groups that can be formed with an equal number of boys and girls in each group.

Answer: 12

Question 8: Find the HCF of 100, 150, and 200.

Answer: 50

Question 9: A mixture contains 60g of sugar and 90g of salt. Use the HCF method to simplify the ratio of sugar to salt.

Answer: 2:3

Question 10: Identify and correct the mistake: Students incorrectly divide 48 and 180 by 6 to find the ratio 8:30, then simplify to 4:15.

Answer: Incorrect; divide both by 6 gives 8:30, which simplifies to 4:15, but the HCF of 48 and 180 is 12, not 6. Correct ratio: 48/12=4, 180/12=15; ratio 4:15.

Question 11: Find the HCF of 56, 98, and 154.

Answer: 14