Answer Keys: Factors & Multiples

Grade 4 Mathematics | FAST Success Kit

Teacher/Parent Resource: This page contains all answers. Keep separate from student materials.
Student Concept Worksheet Answers
1. Factor pairs of 18
(1, 18), (2, 9), (3, 6)
2. Is 23 prime or composite?
Prime
Only factors are 1 and 23
3. First 5 multiples of 7
7, 14, 21, 28, 35
4. All factors of 24
1, 2, 3, 4, 6, 8, 12, 24
5. Circle prime numbers
17, 23, 29
15=3x5, 21=3x7, 27=3x9, 33=3x11
Practice Worksheet Answers

Part A: Factor Pairs

1. 20
(1,20), (2,10), (4,5)
2. 36
(1,36), (2,18), (3,12), (4,9), (6,6)
3. 48
(1,48), (2,24), (3,16), (4,12), (6,8)
4. 56
(1,56), (2,28), (4,14), (7,8)
5. 72
(1,72), (2,36), (3,24), (4,18), (6,12), (8,9)
6. 100
(1,100), (2,50), (4,25), (5,20), (10,10)

Part B: Prime or Composite

7. 17
Prime
8. 27
Composite (3x9)
9. 31
Prime
10. 49
Composite (7x7)
11. 53
Prime
12. 63
Composite (7x9)
13. 71
Prime
14. 91
Composite (7x13)

Part C: Multiples

15. Multiples of 8
8, 16, 24, 32, 40, 48
16. Multiples of 9
9, 18, 27, 36, 45, 54
17. Multiples of 11
11, 22, 33, 44, 55, 66
18. Multiples of 12
12, 24, 36, 48, 60, 72
19. Is 84 a multiple of 7?
Yes (84/7=12)
20. Is 52 a multiple of 6?
No (52/6=8.67)

Part D: GCF

21. GCF of 12 and 18
GCF = 6
12: 1,2,3,4,6,12 | 18: 1,2,3,6,9,18 | Common: 1,2,3,6
22. GCF of 20 and 30
GCF = 10
20: 1,2,4,5,10,20 | 30: 1,2,3,5,6,10,15,30
23. GCF of 24 and 36
GCF = 12
Common: 1,2,3,4,6,12
24. GCF of 16 and 28
GCF = 4
25. GCF of 45 and 60
GCF = 15

Part E: LCM

26. LCM of 4 and 6
LCM = 12
4: 4,8,12,16,20,24 | 6: 6,12,18,24,30,36
27. LCM of 3 and 5
LCM = 15
3: 3,6,9,12,15,18 | 5: 5,10,15,20,25,30
28. LCM of 6 and 8
LCM = 24
29. LCM of 9 and 12
LCM = 36

Part F: Word Problem

30. Maria's bouquets
12 bouquets
GCF of 24 and 36 = 12. Each bouquet: 2 red, 3 yellow.
FAST Practice Quiz Answers
1
B. (1, 24), (2, 12), (3, 8), (4, 6)
All factor pairs of 24: 1x24, 2x12, 3x8, 4x6. Option B includes all four pairs.
2
C. 29
29 has only two factors (1 and 29). 21=3x7, 27=3x9, 33=3x11 are all composite.
3
C. 1 is neither prime nor composite because it has only one factor.
Prime numbers must have EXACTLY two factors. 1 only has one factor (itself), so it's neither.
4
B. 63
63 / 9 = 7 (divides evenly). 56/9=6.2, 65/9=7.2, 68/9=7.6 (don't divide evenly).
5
6
Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. Common: 1,2,3,6. GCF=6.
6
C. Composite, because it has more than 2 factors
The number has 6 factors (1,2,4,5,10,20). More than 2 factors = composite. The number is 20.
7
B. (4, 9) and D. (6, 6)
Katie is missing TWO pairs: (4,9) because 4x9=36, and (6,6) because 6x6=36. Accept either answer.
8
C. 52
52 / 8 = 6.5 (not a whole number). 32/8=4, 48/8=6, 64/8=8 are all multiples of 8.
9
24
Multiples of 6: 6,12,18,24... Multiples of 8: 8,16,24... First common multiple is 24.
10
C. 16 baskets
GCF of 32 and 48 = 16. He can make 16 baskets with 2 red and 3 green apples each.

Scoring Guide

Assessment Total Points Proficient (70%+) Needs Support
Student Concept Worksheet 5 points 4+ correct Review factor vs. multiple
Practice Worksheet 30 points 21+ correct Use arrays for factor pairs
FAST Practice Quiz 10 points 7+ correct Practice with multiplication charts

Common Errors: Thinking 1 is prime, missing factor pairs, confusing factors with multiples, forgetting (n,n) pairs like (6,6) for perfect squares.

FAST Success Kit | Grade 4 | FL B.E.S.T. Standards: MA.4.AR.1.1-1.3