Question 1: List all factor pairs of 36.

Answer: [1,36], [2,18], [3,12], [4,9], [6,6]

Question 2: Calculate the product of the pair factors (3 and 12).

Answer: 36

Question 3: Identify the factor pair of 48 where both factors are even.

Answer: [2, 24], [4, 12], [6, 8]

Question 4: Construct a rectangle on the grid with dimensions corresponding to a factor pair of 20.

Answer: Students draw a rectangle with sides 4 and 5 (or 2 and 10).

Question 5: List the factor pairs of 100 and identify which pair has the greatest difference.

Answer: [1, 100], [2, 50], [4, 25], [5, 20], [10, 10]; Greatest difference: [1, 100]

Question 6: Explain why the pair (6, 10) is not a factor pair of 65.

Answer: Because 6×10 = 60, not 65, so (6, 10) is not a factor pair of 65.

Question 7: Find a factor pair of 81 where both factors are odd numbers.

Answer: [1, 81], [3, 27], [9, 9]

Question 8: A number has exactly 8 factor pairs. What is the smallest possible value of this number?

Answer: 256

Question 9: Identify the factor pairs of 60, and determine which pair is the most balanced (i.e., the closest factors).

Answer: [1, 60], [2, 30], [3, 20], [4, 15], [5, 12], [6, 10]; Most balanced: [6, 10]

Question 10: Challenge: Find a number between 200 and 300 with exactly 12 factor pairs and identify its smallest and largest factors.

Answer: Number: 240; Smallest factor: 1; Largest factor: 240

Question 11: Common Mistake: A student claims 36's factor pairs include (5, 7). Why is this incorrect?

Answer: Because 5×7=35, not 36, so (5, 7) is not a factor pair of 36.