Question 1: Construct a factor tree for the number 36 and write its prime factorization.

Answer: 2^2 * 3^2

Question 2: Use a factor tree to find the prime factors of 48.

Answer: 2^4 * 3

Question 3: Construct a factor tree for 100 and state its prime factorization.

Answer: 2^2 * 5^2

Question 4: Find the prime factors of 75 using a factor tree.

Answer: 3 * 5^2

Question 5: Construct a factor tree for 120 and write its prime factorization.

Answer: 2^3 * 3 * 5

Question 6: Use a factor tree to find the prime factors of 84.

Answer: 2^2 * 3 * 7

Question 7: Construct a factor tree for 90 and state its prime factorization.

Answer: 2 * 3^2 * 5

Question 8: Find the prime factors of 180 using a factor tree.

Answer: 2^2 * 3^2 * 5

Question 9: Construct a factor tree for 144 and write its prime factorization.

Answer: 2^4 * 3^2

Question 10: Use a factor tree to determine the prime factors of 210.

Answer: 2 * 3 * 5 * 7

Question 11: Identify and correct the mistake in this factor tree for 60: (Divide 60 into 6 and 10, then 6 into 2 and 3, 10 into 2 and 5).

Answer: The mistake is that 6 should be factored into 2 and 3, which is correct, but 10 should be factored into 2 and 5, which is also correct. The mistake might be in the presentation or in mislabeling. Alternatively, if students identify the mistake as missing a prime factor, the correction is to ensure the whole factor tree lists only prime factors at the end.