Math worksheet for finding the Greatest Common Factor (GCF) of number pairs.

Sure! Let’s solve each problem step by step. The Greatest Common Factor (GCF) is the largest number that divides two or more numbers evenly.

We’ll find the GCF for each pair using prime factorization or listing factors — whichever is quicker.

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1. GCF(40, 55)

- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 55: 1, 5, 11, 55
→ Common factors: 1, 5
✔ GCF = 5

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2. GCF(33, 44)

- Factors of 33: 1, 3, 11, 33
- Factors of 44: 1, 2, 4, 11, 22, 44
→ Common factors: 1, 11
✔ GCF = 11

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3. GCF(30, 25)

- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 25: 1, 5, 25
→ Common factors: 1, 5
✔ GCF = 5

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4. GCF(40, 18)

- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 18: 1, 2, 3, 6, 9, 18
→ Common factors: 1, 2
✔ GCF = 2

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5. GCF(20, 75)

- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 75: 1, 3, 5, 15, 25, 75
→ Common factors: 1, 5
✔ GCF = 5

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6. GCF(12, 45)

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 45: 1, 3, 5, 9, 15, 45
→ Common factors: 1, 3
✔ GCF = 3

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7. GCF(24, 9)

- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 9: 1, 3, 9
→ Common factors: 1, 3
✔ GCF = 3

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8. GCF(45, 20)

- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 20: 1, 2, 4, 5, 10, 20
→ Common factors: 1, 5
✔ GCF = 5

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9. GCF(36, 18)

- Since 18 divides into 36 evenly (36 ÷ 18 = 2), the GCF is 18.
✔ GCF = 18

*(Alternatively: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; Factors of 18: 1, 2, 3, 6, 9, 18 → common: 18)*

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10. GCF(25, 35)

- Factors of 25: 1, 5, 25
- Factors of 35: 1, 5, 7, 35
→ Common factors: 1, 5
✔ GCF = 5

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## ✔ Final Answers:

1. 5
2. 11
3. 5
4. 2
5. 5
6. 3
7. 3
8. 5
9. 18
10. 5

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Let me know if you’d like to see the prime factorization method for any of these — it’s another great way to find GCFs!