Find the Greatest Common Factor (GCF) for each set of numbers on this math worksheet.

Sure! Let’s solve each problem by finding the Greatest Common Factor (GCF) — the largest number that divides both numbers in each pair evenly.

We’ll go one by one, and I’ll explain how to find the GCF using prime factorization or listing factors, whichever is easiest.

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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)

- 33 = 3 × 11
- 44 = 4 × 11 = 2² × 11
→ Common prime factor: 11
→ GCF = 11

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3. GCF(30, 25)

- 30 = 2 × 3 × 5
- 25 = 5 × 5
→ Common prime factor: 5
→ GCF = 5

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4. GCF(40, 18)

- 40 = 2³ × 5
- 18 = 2 × 3²
→ Common prime factor: 2
→ GCF = 2

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5. GCF(20, 75)

- 20 = 2² × 5
- 75 = 3 × 5²
→ Common prime factor: 5
→ GCF = 5

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6. GCF(12, 45)

- 12 = 2² × 3
- 45 = 3² × 5
→ Common prime factor: 3
→ GCF = 3

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7. GCF(24, 9)

- 24 = 2³ × 3
- 9 = 3²
→ Common prime factor: 3
→ GCF = 3

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8. GCF(45, 20)

- 45 = 3² × 5
- 20 = 2² × 5
→ Common prime factor: 5
→ GCF = 5

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9. GCF(36, 18)

- 36 = 2² × 3²
- 18 = 2 × 3²
→ Common prime factors: 2¹ × 3² → 2 × 9 = 18
→ GCF = 18

*(Note: Since 18 divides 36 evenly, the GCF is just 18.)*

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10. GCF(25, 35)

- 25 = 5²
- 35 = 5 × 7
→ Common prime factor: 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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## 📝 Tip for Finding GCF:
- List all factors of both numbers and pick the largest common one.
- Or use prime factorization: break each number into primes, then multiply the common primes with the lowest exponent.

Let me know if you want a visual diagram or step-by-step breakdown for any specific problem!