Question 1: Find the Greatest Common Factor of 24 and 36.

Answer: 12

Question 2: Calculate the GCF of 48, 64, and 80.

Answer: 16

Question 3: Find the GCF of 45 and 60.

Answer: 15

Question 4: Determine the GCF of 14 and 21.

Answer: 7

Question 5: Explain the steps to find the GCF of 36 and 54.

Answer: Prime factorize both numbers (36 = 2^2 * 3^2, 54 = 2 * 3^3). The common factors are 2 and 3, with the lowest powers 2^1 and 3^2. GCF = 2 * 3^2 = 2 * 9 = 18.

Question 6: A bakery makes packets containing 48 and 60 cookies. What is the largest number of packets they can make so that each packet has the same number of cookies?

Answer: 12

Question 7: Find the GCF of 81 and 99.

Answer: 9

Question 8: Simplify the fraction 42/56 using the GCF.

Answer: Divide numerator and denominator by 14: 42/14=3, 56/14=4, so simplified fraction = 3/4

Question 9: Identify the common mistake made when finding the GCF of 20 and 30 if a student says it is 10.

Answer: The mistake is assuming the GCF is the largest common multiple or misidentifying common factors; the correct GCF is 10, which is correct here. The error could be miscalculating or missing the common factors altogether.

Question 10: Find the GCF of 56 and 48 and explain if 8 can be the GCF.

Answer: The GCF is 8 because 8 divides both 56 and 48 exactly. However, since 8 is a common factor, but not the greatest, the GCF is 14 for 56 and 48? No, 14 does not divide 48 evenly; so GCF is 8.

Question 11: Compute the GCF of 100 and 125. Then, use it to simplify the fraction 100/125.

Answer: GCF of 100 and 125 is 25. Divide numerator and denominator by 25: 100/25=4, 125/25=5. Simplified fraction = 4/5.