Math worksheet for practicing finding common factors and greatest common factors.

Problem Overview:

The worksheet asks us to:
1. List at least 2 common factors for each set of numbers.
2. Find the Greatest Common Factor (GCF) for each set of numbers.

We will solve both parts step by step.

---

Part 1: List at least 2 common factors for each set of numbers.

#### Step-by-Step Solution:

1. Set 1: 12, 24
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Common factors: \(1, 2, 3, 4, 6, 12\)
- At least 2 common factors: 2, 3

2. Set 2: 18, 30
- Factors of 18: \(1, 2, 3, 6, 9, 18\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 2, 3, 6\)
- At least 2 common factors: 2, 3

3. Set 3: 16, 20
- Factors of 16: \(1, 2, 4, 8, 16\)
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Common factors: \(1, 2, 4\)
- At least 2 common factors: 2, 4

4. Set 4: 24, 32
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Factors of 32: \(1, 2, 4, 8, 16, 32\)
- Common factors: \(1, 2, 4, 8\)
- At least 2 common factors: 2, 4

5. Set 5: 36, 45
- Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Common factors: \(1, 3, 9\)
- At least 2 common factors: 3, 9

6. Set 6: 40, 60
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Factors of 60: \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)
- Common factors: \(1, 2, 4, 5, 10, 20\)
- At least 2 common factors: 2, 5

7. Set 7: 45, 90
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Factors of 90: \(1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90\)
- Common factors: \(1, 3, 5, 9, 15, 45\)
- At least 2 common factors: 3, 5

8. Set 8: 60, 90
- Factors of 60: \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)
- Factors of 90: \(1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90\)
- Common factors: \(1, 2, 3, 5, 6, 10, 15, 30\)
- At least 2 common factors: 3, 5

9. Set 9: 15, 30
- Factors of 15: \(1, 3, 5, 15\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 3, 5, 15\)
- At least 2 common factors: 3, 5

10. Set 10: 20, 30
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 2, 5, 10\)
- At least 2 common factors: 2, 5

---

Part 2: Find the Greatest Common Factor (GCF) for each set of numbers.

#### Step-by-Step Solution:

1. Set 1: 15, 24
- Factors of 15: \(1, 3, 5, 15\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Common factors: \(1, 3\)
- GCF: 3

2. Set 2: 24, 30
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 2, 3, 6\)
- GCF: 6

3. Set 3: 30, 40
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Common factors: \(1, 2, 5, 10\)
- GCF: 10

4. Set 4: 16, 20
- Factors of 16: \(1, 2, 4, 8, 16\)
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Common factors: \(1, 2, 4\)
- GCF: 4

5. Set 5: 25, 45
- Factors of 25: \(1, 5, 25\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Common factors: \(1, 5\)
- GCF: 5

6. Set 6: 18, 45
- Factors of 18: \(1, 2, 3, 6, 9, 18\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Common factors: \(1, 3, 9\)
- GCF: 9

7. Set 7: 20, 50
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Factors of 50: \(1, 2, 5, 10, 25, 50\)
- Common factors: \(1, 2, 5, 10\)
- GCF: 10

8. Set 8: 30, 45
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Common factors: \(1, 3, 5, 15\)
- GCF: 15

9. Set 9: 25, 30
- Factors of 25: \(1, 5, 25\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 5\)
- GCF: 5

10. Set 10: 10, 60
- Factors of 10: \(1, 2, 5, 10\)
- Factors of 60: \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)
- Common factors: \(1, 2, 5, 10\)
- GCF: 10

---

Final Answers:

#### Part 1: Common Factors
1. 2, 3
2. 2, 3
3. 2, 4
4. 2, 4
5. 3, 9
6. 2, 5
7. 3, 5
8. 3, 5
9. 3, 5
10. 2, 5

#### Part 2: Greatest Common Factor (GCF)
1. 3
2. 6
3. 10
4. 4
5. 5
6. 9
7. 10
8. 15
9. 5
10. 10

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{Common Factors} \\
1. & 2, 3 \\
2. & 2, 3 \\
3. & 2, 4 \\
4. & 2, 4 \\
5. & 3, 9 \\
6. & 2, 5 \\
7. & 3, 5 \\
8. & 3, 5 \\
9. & 3, 5 \\
10. & 2, 5 \\
\\
\text{Part 2:} & \text{Greatest Common Factor (GCF)} \\
1. & 3 \\
2. & 6 \\
3. & 10 \\
4. & 4 \\
5. & 5 \\
6. & 9 \\
7. & 10 \\
8. & 15 \\
9. & 5 \\
10. & 10 \\
\end{array}
}
\]