Factors Worksheet for students to practice finding factors, common factors, and greatest common factors.

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

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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 of the following:

1. 16:
Factors: 1, 2, 4, 8, 16
→ 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:
(Repeated) → 1, 3, 5

✔ Answer Key – Part 1:
1. 1, 2, 4
2. 1, 3, 5
3. 1, 3, 5
4. 1, 2, 3
5. 1, 2, 3
6. 1, 2, 3
7. 1, 2, 4
8. 1, 3, 5

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

We find factors that both numbers share.

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

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

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

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

✔ Answer Key – Part 2:
1. 1, 2
2. 1, 2
3. 1, 2
4. 1, 2
5. 1, 2
6. 1, 2
7. 1, 2
8. 1, 2

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Part 3: Find the Greatest Common Factor (GCF) for each set

The GCF is the largest factor that both numbers share.

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

2. 12, 4
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 4: 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
→ 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
- 40 divides evenly into 80 → 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 into 60 → GCF = 10

✔ Answer Key – Part 3:
1. 14
2. 4
3. 6
4. 2
5. 2
6. 40
7. 2
8. 10

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✔ Final Answer Summary:

#### Part 1: At least 3 factors
1. 1, 2, 4
2. 1, 3, 5
3. 1, 3, 5
4. 1, 2, 3
5. 1, 2, 3
6. 1, 2, 3
7. 1, 2, 4
8. 1, 3, 5

#### Part 2: At least 2 common factors
1. 1, 2
2. 1, 2
3. 1, 2
4. 1, 2
5. 1, 2
6. 1, 2
7. 1, 2
8. 1, 2

#### Part 3: Greatest Common Factor (GCF)
1. 14
2. 4
3. 6
4. 2
5. 2
6. 40
7. 2
8. 10

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🔍 Explanation Tips:

- A factor is a number that divides another number without a remainder.
- Common factors are factors shared by two or more numbers.
- The Greatest Common Factor (GCF) is the largest of those common factors.
- You can use prime factorization or listing factors to find GCF.

Let me know if you'd like this in printable format or with steps shown!