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

Answer: 2, 2, 2, 2, 3

Question 2: Build a factor tree for 120 and identify all prime factors.

Answer: 2, 2, 2, 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 225. What are its prime factors?

Answer: 3, 3, 5, 5

Question 5: Explain why the prime factors obtained from a factor tree are unique, even if the tree is drawn differently.

Answer: Prime factorization is unique (Fundamental Theorem of Arithmetic), so regardless of how the factor tree is drawn, the prime factors will always be the same, just in different orders.

Question 6: Construct a factor tree for 360 and list all prime factors.

Answer: 2, 2, 2, 3, 3, 5

Question 7: A student draws a factor tree for 84 and lists the factors as 2, 2, 3, 14. Identify the mistake and correct the factorization.

Answer: 14 is not a prime number, so it should be further factorized into 2 and 7. Correct prime factors: 2, 2, 3, 7.

Question 8: Construct a factor tree for 252 and determine its prime factors.

Answer: 2, 2, 3, 3, 7

Question 9: Using the factor tree method, find the prime factors of 315.

Answer: 3, 3, 3, 5, 7

Question 10: Construct a factor tree for 100 and list its prime factors. Then, explain the significance of the tree structure in understanding prime factorization.

Answer: Prime factors: 2, 2, 5, 5. The tree shows how the number is broken down into prime components, illustrating the process of prime factorization visually and ensuring understanding of the fundamental theorem.

Question 11: Challenge: Construct a factor tree for 1029 and determine its prime factors. Explain your steps.

Answer: 1029 ÷ 3 = 343; 343 ÷ 7 = 49; 49 ÷ 7 = 7; Prime factors: 3, 7, 7, 7.