Question 1: Factorise the numerical expression: 24x + 36.

Answer: 12(2x + 3)

Question 2: Find the common factor of 48 and 60.

Answer: 12

Question 3: Factorise: 35a + 14b.

Answer: 7(5a + 2b)

Question 4: Calculate the greatest common divisor (GCD) of 81 and 54.

Answer: 27

Question 5: Factorise: 18x^2 + 27x.

Answer: 9x(2x + 3)

Question 6: A baker makes 60 cookies and 90 muffins. Find the largest number of equal gift boxes you can pack with the same number of each item, using all items.

Answer: 15

Question 7: Construct an expression for the total cost if each notebook costs 8 dollars and each pen costs 2 dollars, factorising the total cost in terms of the number of notebooks.

Answer: 2(4n + 1n) or 2(4n + n)

Question 8: Identify the common factor in 56, 84, and 98.

Answer: 14

Question 9: A gardener plants rows of trees, with 40 trees in each row. If there are 120 trees in total, what is the maximum number of trees per row that divides evenly into the total?

Answer: 40

Question 10: Find the common factor of 81, 117, and 135 and state the steps involved.

Answer: 3; factors: 81=3^4, 117=3×3×13, 135=3^3×5; common factor=3

Question 11: A factory produces 120 units of product A and 150 units of product B each day. What is the largest number of equal batches they can produce daily, using all units?

Answer: 30