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 factor pairs (4, 9) and (3, 12).

Answer: 36 and 36

Question 3: If a number has factor pairs (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), what is the original number?

Answer: 48

Question 4: Plot the graph of y=2x on the grid. Draw and label at least 5 points.

Answer: Points (1,2), (2,4), (3,6), (4,8), (5,10)

Question 5: Construct a triangle on the grid with side lengths corresponding to a factor pair of 20.

Answer: Construct sides of 4 and 5, which are factor pairs of 20

Question 6: Identify the error: A student says the factor pairs of 28 are (1,28), (2,14), (4,7). Is this correct? Explain and correct if necessary.

Answer: Incorrect. Correct factor pairs of 28 are (1,28), (2,14), (4,7). The statement is correct; no correction needed.

Question 7: Find all factor pairs of 100. List them.

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

Question 8: A number has exactly 8 factor pairs. What is the possible number of its prime factors? Explain briefly.

Answer: It likely has 3 prime factors or a perfect square with 4 prime factors, as numbers with 8 factor pairs typically have complex prime factorization.

Question 9: Determine whether 54 is a perfect square based on its factor pairs. Show your reasoning.

Answer: No, because its factor pairs include (1,54), (2,27), (3,18), (6,9). Since 6×9=54, not a perfect square.

Question 10: Challenge: Find a number between 50 and 60 that has exactly 6 factor pairs. Justify your answer.

Answer: Number 60 has factor pairs: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10). Total of 6 pairs.