Grade 5 Factoring Worksheets: Greatest Common Factor (GCF) (1-100 ... - Free Printable

Let's solve each problem on the Greatest Common Factor (GCF) worksheet step by step. The goal is to find the largest number that divides both numbers in each pair evenly.

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🔷 How to Find GCF:

We can use:
- Listing factors, or
- Prime factorization, or
- Euclidean algorithm (for larger numbers)

We'll use listing factors for simplicity.

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✔ Problem 1: 58 and 26

Factors of 58:
1, 2, 29, 58

Factors of 26:
1, 2, 13, 26

Common factors: 1, 2
→ GCF = 2

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✔ Problem 2: 50 and 65

Factors of 50:
1, 2, 5, 10, 25, 50

Factors of 65:
1, 5, 13, 65

Common factors: 1, 5
→ GCF = 5

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✔ Problem 3: 70 and 2

Factors of 70:
1, 2, 5, 7, 10, 14, 35, 70

Factors of 2:
1, 2

Common factors: 1, 2
→ GCF = 2

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✔ Problem 4: 21 and 60

Factors of 21:
1, 3, 7, 21

Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Common factors: 1, 3
→ GCF = 3

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✔ Problem 5: 44 and 48

Factors of 44:
1, 2, 4, 11, 22, 44

Factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors: 1, 2, 4
→ GCF = 4

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✔ Problem 6: 33 and 48

Factors of 33:
1, 3, 11, 33

Factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors: 1, 3
→ GCF = 3

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✔ Problem 7: 77 and 33

Factors of 77:
1, 7, 11, 77

Factors of 33:
1, 3, 11, 33

Common factors: 1, 11
→ GCF = 11

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✔ Problem 8: 80 and 25

Factors of 80:
1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Factors of 25:
1, 5, 25

Common factors: 1, 5
→ GCF = 5

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✔ Problem 9: 70 and 20

Factors of 70:
1, 2, 5, 7, 10, 14, 35, 70

Factors of 20:
1, 2, 4, 5, 10, 20

Common factors: 1, 2, 5, 10
→ GCF = 10

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✔ Problem 10: 65 and 70

Factors of 65:
1, 5, 13, 65

Factors of 70:
1, 2, 5, 7, 10, 14, 35, 70

Common factors: 1, 5
→ GCF = 5

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✔ Final Answers:

| Problem | Numbers | GCF |
|--------|--------|-----|
| 1 | 58, 26 | 2 |
| 2 | 50, 65 | 5 |
| 3 | 70, 2 | 2 |
| 4 | 21, 60 | 3 |
| 5 | 44, 48 | 4 |
| 6 | 33, 48 | 3 |
| 7 | 77, 33 | 11 |
| 8 | 80, 25 | 5 |
| 9 | 70, 20 | 10 |
| 10 | 65, 70 | 5 |

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📝 Summary:

To find the GCF:
1. List all factors of each number.
2. Identify common factors.
3. Choose the greatest one.

This method works well for smaller numbers. For larger ones, prime factorization or the Euclidean algorithm is more efficient.

Let me know if you'd like a version with prime factorization steps!