Class Practice - Finding the GCF

What is the GCF of 24 and 36?

• 6

• 18

• 24

• 12

Answer explanation

To find the GCF of 24 and 36, list the factors: 24 (1, 2, 3, 4, 6, 8, 12, 24) and 36 (1, 2, 3, 4, 6, 9, 12, 18, 36). The largest common factor is 12, making it the GCF.

Find the GCF of 18, 24, and 30.

• 18

• 12

• 24

• 6

Answer explanation

To find the GCF of 18, 24, and 30, we list their factors: 18 (1, 2, 3, 6, 9, 18), 24 (1, 2, 3, 4, 6, 8, 12, 24), and 30 (1, 2, 3, 5, 6, 10, 15, 30). The largest common factor is 6.

A gardener has 36 red roses and 48 yellow roses. What is the greatest number of bouquets he can make if each bouquet has the same number of roses?

• 6

• 12

• 24

• 18

Answer explanation

To find the greatest number of bouquets, we need the greatest common divisor (GCD) of 36 and 48. The GCD is 12, meaning the gardener can make 12 bouquets with each containing 3 red and 4 yellow roses.

The lengths of three pieces of ribbon are 12, 18, and 30 inches. What is the GCF of these lengths?

• 12

• 18

• 24

• 6

Answer explanation

To find the GCF of 12, 18, and 30, we list the factors: 12 (1, 2, 3, 4, 6, 12), 18 (1, 2, 3, 6, 9, 18), and 30 (1, 2, 3, 5, 6, 10, 15, 30). The largest common factor is 6.

What is the GCF of 32 and 48?

• 8

• 16

• 4

• 12

Two friends are making gift bags. One has 20 candies and the other has 30 candies. What is the maximum number of bags they can make with the same number of candies in each?

• 15

• 25

• 10

• 5

Answer explanation

To find the maximum number of bags with the same number of candies, we need the greatest common divisor (GCD) of 20 and 30. The GCD is 10, meaning they can make 10 bags with 2 candies each.

Calculate the GCF of 15 and 25.

• 15

• 20

• 10

• 5

Answer explanation

The GCF (Greatest Common Factor) of 15 and 25 is 5, as it is the largest number that divides both without leaving a remainder. The factors of 15 are 1, 3, 5, 15 and for 25 are 1, 5, 25. The common factor is 5.

A recipe requires 8 cups of flour and 12 cups of sugar. If you want to make the largest number of batches with the same amount of each ingredient, what is the GCF of the two amounts?

• 10

• 6

• 4

• 2

Answer explanation

To find the GCF of 8 cups of flour and 12 cups of sugar, we list the factors: 8 (1, 2, 4, 8) and 12 (1, 2, 3, 4, 6, 12). The largest common factor is 4, making it the GCF for the ingredients.

Find the GCF of 42, 56, and 98.

• 14

• 28

• 7

• 21

Answer explanation

To find the GCF of 42, 56, and 98, we can list the factors: 42 (1, 2, 3, 6, 7, 14, 21, 42), 56 (1, 2, 4, 7, 8, 14, 28, 56), and 98 (1, 2, 7, 14, 49, 98). The largest common factor is 14.

A school is organizing a field trip for 60 students and 90 parents. What is the largest group size they can form if each group has the same number of students and parents?

• 45

• 75

• 15

• 30

Answer explanation

To find the largest group size with equal students and parents, we need the greatest common divisor (GCD) of 60 and 90. The GCD is 30, allowing for groups of 30 students and 30 parents, which is the largest possible equal grouping.