Worksheet for finding the Greatest Common Factor (GCF) of number sets.

To solve the problem of finding the Greatest Common Factor (GCF) for each set of numbers, we need to determine the largest number that divides all the numbers in each set without leaving a remainder. Here's how we can approach each set step by step:

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Step-by-Step Solution:

#### 1. 15, 30, 25
- Factors of 15: \(1, 3, 5, 15\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Factors of 25: \(1, 5, 25\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 2. 25, 40, 35
- Factors of 25: \(1, 5, 25\)
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Factors of 35: \(1, 5, 7, 35\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 3. 28, 36, 40
- Factors of 28: \(1, 2, 4, 7, 14, 28\)
- Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Common factors: \(1, 2, 4\)
- Greatest Common Factor: 4

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

#### 5. 45, 25, 35
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Factors of 25: \(1, 5, 25\)
- Factors of 35: \(1, 5, 7, 35\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 6. 24, 36, 45
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Common factors: \(1, 3\)
- Greatest Common Factor: 3

#### 7. 55, 40, 25
- Factors of 55: \(1, 5, 11, 55\)
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Factors of 25: \(1, 5, 25\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 8. 20, 25, 30
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Factors of 25: \(1, 5, 25\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 9. 12, 40, 50
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Factors of 50: \(1, 2, 5, 10, 25, 50\)
- Common factors: \(1, 2\)
- Greatest Common Factor: 2

#### 10. 27, 45, 15
- Factors of 27: \(1, 3, 9, 27\)
- Factors of 45: \(1, 3, 5, 9, 15, 45\)
- Factors of 15: \(1, 3, 5, 15\)
- Common factors: \(1, 3\)
- Greatest Common Factor: 3

#### 11. 20, 60, 90
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- 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: \(1, 2, 5, 10\)
- Greatest Common Factor: 10

#### 12. 35, 70, 120
- Factors of 35: \(1, 5, 7, 35\)
- Factors of 70: \(1, 2, 5, 7, 10, 14, 35, 70\)
- Factors of 120: \(1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 13. 55, 100, 135
- Factors of 55: \(1, 5, 11, 55\)
- Factors of 100: \(1, 2, 4, 5, 10, 20, 25, 50, 100\)
- Factors of 135: \(1, 3, 5, 9, 15, 27, 45, 135\)
- Common factors: \(1, 5\)
- Greatest Common Factor: 5

#### 14. 12, 50, 72
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 50: \(1, 2, 5, 10, 25, 50\)
- Factors of 72: \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\)
- Common factors: \(1, 2\)
- Greatest Common Factor: 2

#### 15. 80, 50, 100
- Factors of 80: \(1, 2, 4, 5, 8, 10, 16, 20, 40, 80\)
- Factors of 50: \(1, 2, 5, 10, 25, 50\)
- Factors of 100: \(1, 2, 4, 5, 10, 20, 25, 50, 100\)
- Common factors: \(1, 2, 5, 10\)
- Greatest Common Factor: 10

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Final Answers:

1. 5
2. 5
3. 4
4. 10
5. 5
6. 3
7. 5
8. 5
9. 2
10. 3
11. 10
12. 5
13. 5
14. 2
15. 10

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Boxed Answer:

\[
\boxed{5, 5, 4, 10, 5, 3, 5, 5, 2, 3, 10, 5, 5, 2, 10}
\]