Multiples and Factors Worksheets - 25 Interactive, Printable ... - Free Printable

Let's solve the Factors Worksheet step by step and explain each part.

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Part 1: List at least 3 factors for each number

We need to list at least 3 factors (numbers that divide evenly into the given number) for each.

1. 16
Factors: 1, 2, 4, 8, 16 → Any three: 1, 2, 4

2. 15
Factors: 1, 3, 5, 15 → 1, 3, 5

3. 45
Factors: 1, 3, 5, 9, 15, 45 → 1, 3, 5

4. 18
Factors: 1, 2, 3, 6, 9, 18 → 1, 2, 3

5. 24
Factors: 1, 2, 3, 4, 6, 8, 12, 24 → 1, 2, 3

6. 30
Factors: 1, 2, 3, 5, 6, 10, 15, 30 → 1, 2, 3

7. 32
Factors: 1, 2, 4, 8, 16, 32 → 1, 2, 4

8. 15
Same as #2 → 1, 3, 5

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Part 2: List at least 2 common factors for each set of numbers

Common factors are numbers that divide both numbers in the pair.

1. 16, 20
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common: 1, 2, 4 → Two: 1, 2

2. 12, 34
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 34: 1, 2, 17, 34
- Common: 1, 2 → 1, 2

3. 42, 18
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common: 1, 2, 3, 6 → 1, 2

4. 18, 14
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 14: 1, 2, 7, 14
- Common: 1, 2 → 1, 2

5. 24, 32
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 32: 1, 2, 4, 8, 16, 32
- Common: 1, 2, 4, 8 → 1, 2

6. 30, 46
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 46: 1, 2, 23, 46
- Common: 1, 2 → 1, 2

7. 38, 50
- Factors of 38: 1, 2, 19, 38
- Factors of 50: 1, 2, 5, 10, 25, 50
- Common: 1, 2 → 1, 2

8. 10, 20
- Factors of 10: 1, 2, 5, 10
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common: 1, 2, 5, 10 → 1, 2

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Part 3: Find the Greatest Common Factor (GCF)

The GCF is the largest number that divides both numbers.

1. 14, 28
- Factors of 14: 1, 2, 7, 14
- Factors of 28: 1, 2, 4, 7, 14, 28
- Common: 1, 2, 7, 14 → GCF = 14

2. 12, 4
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 4: 1, 2, 4
- Common: 1, 2, 4 → GCF = 4

3. 42, 6
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 6: 1, 2, 3, 6
- Common: 1, 2, 3, 6 → GCF = 6

4. 16, 30
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common: 1, 2 → GCF = 2

5. 30, 32
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 32: 1, 2, 4, 8, 16, 32
- Common: 1, 2 → GCF = 2

6. 80, 40
- Since 40 divides 80 exactly (80 ÷ 40 = 2), GCF = 40

7. 38, 50
- Factors of 38: 1, 2, 19, 38
- Factors of 50: 1, 2, 5, 10, 25, 50
- Common: 1, 2 → GCF = 2

8. 10, 60
- 10 divides 60 exactly (60 ÷ 10 = 6), so GCF = 10

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✔ Final Answers:

#### Part 1: At least 3 factors
1. 16 → 1, 2, 4
2. 15 → 1, 3, 5
3. 45 → 1, 3, 5
4. 18 → 1, 2, 3
5. 24 → 1, 2, 3
6. 30 → 1, 2, 3
7. 32 → 1, 2, 4
8. 15 → 1, 3, 5

#### Part 2: At least 2 common factors
1. 16, 20 → 1, 2
2. 12, 34 → 1, 2
3. 42, 18 → 1, 2
4. 18, 14 → 1, 2
5. 24, 32 → 1, 2
6. 30, 46 → 1, 2
7. 38, 50 → 1, 2
8. 10, 20 → 1, 2

#### Part 3: GCF
1. 14, 28 → 14 is the GCF
2. 12, 4 → 4 is the GCF
3. 42, 6 → 6 is the GCF
4. 16, 30 → 2 is the GCF
5. 30, 32 → 2 is the GCF
6. 80, 40 → 40 is the GCF
7. 38, 50 → 2 is the GCF
8. 10, 60 → 10 is the GCF

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