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

Worksheet titled "Greatest Common Factor" with 10 problems asking to find the GCF for each set of numbers, including examples like GCF(40, 55) and GCF(12, 45), with a space for the student's name at the top and the 15Worksheets.com logo at the bottom.

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Let's solve each problem step by step to find the Greatest Common Factor (GCF) for each pair of numbers. The GCF is the largest number that divides both numbers without leaving a remainder.

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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)

- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6, 9, 18
- GCF = 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. GCF(40, 55) = 5
2. GCF(33, 44) = 11
3. GCF(30, 25) = 5
4. GCF(40, 18) = 2
5. GCF(20, 75) = 5
6. GCF(12, 45) = 3
7. GCF(24, 9) = 3
8. GCF(45, 20) = 5
9. GCF(36, 18) = 18
10. GCF(25, 35) = 5

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Let me know if you'd like a visual explanation using prime factorization or the Euclidean algorithm!

Parent Tip: Review the logic above to help your child master the concept of finding the gcf worksheet.

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