Question 1: Find the prime factorization of 48.

Answer: 2^4 * 3

Question 2: Find the prime factorization of 72.

Answer: 2^3 * 3^2

Question 3: Calculate the HCF of 48 and 72 using prime factors.

Answer: 24

Question 4: Determine the HCF of 60 and 90 by prime factorization.

Answer: 30

Question 5: Construct the prime factorization of 84.

Answer: 2^2 * 3 * 7

Question 6: Find the HCF of 84 and 126 using prime factors.

Answer: 42

Question 7: A box contains 36 red sweets and 48 blue sweets. Find the largest number of sweets you can pack equally in boxes so that each box has the same number of each color, using prime factors.

Answer: 12

Question 8: Calculate the HCF of 150 and 200 using prime factor method.

Answer: 50

Question 9: Find the HCF of 84, 126, and 210 using prime factors.

Answer: 14

Question 10: Identify and correct the mistake: Find the HCF of 48 and 60, where the prime factorization of 48 is 2^4 * 3 and of 60 is 2^2 * 3 * 5. The answer is 12.

Answer: The mistake is including 5 in the HCF; the correct HCF is 2^2 * 3 = 12.

Question 11: Challenge: Find the HCF of 210 and 350 using prime factors, and explain your steps.

Answer: Prime factorizations: 210 = 2 * 3 * 5 * 7; 350 = 2 * 5^2 * 7. HCF = 2 * 5 * 7 = 70.