Question 1: Construct a factor tree for the number 48 and find its prime factors.

Answer: 2, 2, 2, 2, 3

Question 2: Determine the prime factorization of 90 using a factor tree.

Answer: 2, 3, 3, 5

Question 3: Using a factor tree, find the prime factors of 84.

Answer: 2, 2, 3, 7

Question 4: Construct a factor tree for 100 and identify its prime factors.

Answer: 2, 2, 5, 5

Question 5: Construct a factor tree for 125 and find its prime factors.

Answer: 5, 5, 5

Question 6: Explain why the prime factors of 72 are 2 and 3, and show the factor tree.

Answer: Prime factors of 72 are 2 and 3 because 72 = 2^3 * 3^2, which can be shown in the factor tree by repeatedly dividing by 2 and 3.

Question 7: A number's prime factorization is 2^2 * 5 * 7. Construct its factor tree.

Answer: Start with the number 140. Divide by 2 to get 70, then again by 2 to get 35, then divide 35 by 5 to get 7. Prime factors: 2, 2, 5, 7.

Question 8: Construct a factor tree for 144 and find all prime factors.

Answer: 2, 2, 2, 2, 3, 3

Question 9: Construct a factor tree for 210 and list its prime factors.

Answer: 2, 3, 5, 7

Question 10: Identify and correct the mistake in this incomplete factor tree: 60 → (60 ÷ 2 = 30) → (30 ÷ 4 = 7.5).

Answer: The mistake is dividing 30 by 4; 4 is not a prime factor of 30. Correct division should be by 2 or 3, for example 30 ÷ 2 = 15.

Question 11: Using a factor tree, find the prime factors of 180 and verify your work.

Answer: 2, 2, 3, 3, 5