Questions on Greatest Common Factor (GCF) - Using Lists & Factor Trees
Multiple choice questions (with five alternatives each) for Grade 6 students, focusing on the Greatest Common Factor (GCF) using lists and factor trees, all presented in real-life hypothetical situations. The answer key with explanations is at the end.
Greatest Common Factor (Using Lists & Factor Trees) – Grade 6
Questions
1. Mia has 18 apples and 24 oranges. She wants to divide them into the largest possible equal groups without mixing fruit. What is the greatest number of groups she can make?
A) 2
B) 3
C) 6
D) 8
E) 12
2. Ethan has 16 red beads and 36 blue beads. What is the greatest number of equal bead necklaces he can make using all beads?
A) 2
B) 4
C) 8
D) 6
E) 10
3. A gardener planted 30 roses and 45 tulips. She wants to group them with the same number of flowers in each bed. What is the greatest number of flower beds she can make?
A) 3
B) 5
C) 10
D) 15
E) 30
4. A coach has 42 soccer balls and 56 cones. He wants to make training kits with the same number of each item. What is the greatest number of kits he can make?
A) 6
B) 7
C) 8
D) 12
E) 14
5. Olivia has 60 stickers and Liam has 84 stickers. They want to pack their stickers into identical packets using all of them. What’s the GCF of 60 and 84?
A) 2
B) 4
C) 6
D) 12
E) 24
6. A musician has two types of drumsticks: 48 wood and 64 plastic. He wants to bundle them into sets with equal numbers of each type. What’s the largest number of complete sets he can make?
A) 4
B) 6
C) 8
D) 12
E) 16
7. A baker has 72 chocolate cookies and 90 vanilla cookies. What’s the greatest number of boxes he can fill evenly with both types?
A) 6
B) 9
C) 12
D) 18
E) 36
8. Two printers print 36 and 54 pages per hour. They start at the same time. After how many pages will they finish printing the same number at once? (Hint: Use GCF to simplify a ratio.)
A) 6
B) 9
C) 12
D) 18
E) 90
9. Emma has 40 pencils and Ava has 100 pens. They want to donate them in identical kits. What’s the GCF of 40 and 100?
A) 5
B) 10
C) 15
D) 20
E) 40
10. Two runners are training. One runs 66 miles a week, the other runs 99. What’s the greatest number of equal-mile training sessions they can divide their runs into?
A) 3
B) 6
C) 9
D) 11
E) 33
11. Liam has 16 candies and Noah has 28. They want to put them in identical party bags using all of the candies. What is the GCF?
A) 2
B) 4
C) 6
D) 8
E) 14
12. A farmer has 27 sheep and 36 goats. What is the greatest number of pens he can build, with the same number of each animal in each pen?
A) 3
B) 6
C) 9
D) 12
E) 18
13. Two friends collect 48 and 60 toy cars. What is the greatest number of shelves needed so that each shelf holds the same number of each friend's toy cars?
A) 6
B) 8
C) 10
D) 12
E) 24
14. A school is organizing students: 24 sixth-graders and 36 seventh-graders. What’s the largest number of teams with equal students from each grade?
A) 3
B) 6
C) 8
D) 12
E) 18
15. A florist has 50 red and 70 yellow flowers. She wants to make identical bouquets using all flowers. What’s the GCF?
A) 2
B) 5
C) 10
D) 20
E) 25
16. A class has 84 colored pencils and 108 markers. What’s the greatest number of art kits the teacher can make with equal amounts?
A) 6
B) 8
C) 12
D) 24
E) 36
17. A parade has 96 dancers and 120 drummers. How many groups can be formed so that each has the same number of dancers and drummers?
A) 8
B) 12
C) 16
D) 24
E) 30
18. A game has 27 red tiles and 81 blue tiles. What’s the GCF of 27 and 81?
A) 3
B) 9
C) 27
D) 54
E) 81
19. Jake has 55 marbles and Max has 99. They want to put them into as many identical jars as possible. What’s the GCF?
A) 11
B) 9
C) 5
D) 3
E) 1
20. Two choirs are rehearsing: one sings 63 songs, the other 84. What’s the greatest number of identical playlists they can create, using all songs?
A) 7
B) 9
C) 14
D) 21
E) 28
Answer Key with Explanations
Q# |
Answer |
Explanation |
|---|---|---|
1 |
C) 6 |
GCF of 18 and 24 = 6 (common factors: 1, 2, 3, 6) |
2 |
C) 8 |
GCF of 16 and 36 = 4 |
3 |
D) 15 |
GCF of 30 and 45 = 15 |
4 |
B) 7 |
GCF of 42 and 56 = 14 |
5 |
D) 12 |
GCF of 60 and 84 = 12 |
6 |
C) 8 |
GCF of 48 and 64 = 16 |
7 |
D) 18 |
GCF of 72 and 90 = 18 |
8 |
A) 6 |
GCF of 36 and 54 = 18 → for simplification |
9 |
B) 20 |
GCF of 40 and 100 = 20 |
10 |
D) 33 |
GCF of 66 and 99 = 33 |
11 |
A) 4 |
GCF of 16 and 28 = 4 |
12 |
C) 9 |
GCF of 27 and 36 = 9 |
13 |
D) 12 |
GCF of 48 and 60 = 12 |
14 |
B) 6 |
GCF of 24 and 36 = 6 |
15 |
C) 10 |
GCF of 50 and 70 = 10 |
16 |
C) 12 |
GCF of 84 and 108 = 12 |
17 |
D) 24 |
GCF of 96 and 120 = 24 |
18 |
C) 27 |
GCF of 27 and 81 = 27 |
19 |
A) 11 |
GCF of 55 and 99 = 11 |
20 |
C) 21 |
GCF of 63 and 84 = 21 |
Share Online!
