Greatest common factor homework worksheet with multiple practice problems.

Let's solve each of these Greatest Common Factor (GCF) problems step by step. The GCF of two numbers is the largest number that divides both of them without leaving a remainder.

We'll use prime factorization or listing factors to find the GCF for each pair.

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Column 1:

#### 1. 27, 63
- Factors of 27: 1, 3, 9, 27
- Factors of 63: 1, 3, 7, 9, 21, 63
- Common factors: 1, 3, 9 → GCF = 9 ✔ (Already given)

#### 2. 77, 66
- 77 = 7 × 11
- 66 = 6 × 11 = 2 × 3 × 11
- Common factor: 11 → GCF = 11

#### 3. 10, 12
- 10 = 2 × 5
- 12 = 2² × 3
- Common: 2 → GCF = 2

#### 4. 20, 16
- 20 = 2² × 5
- 16 = 2⁴
- Common: 2² = 4 → GCF = 4

#### 5. 9, 21
- 9 = 3²
- 21 = 3 × 7
- Common: 3 → GCF = 3

#### 6. 18, 27
- 18 = 2 × 3²
- 27 = 3³
- Common: 3² = 9 → GCF = 9

#### 7. 20, 24
- 20 = 2² × 5
- 24 = 2³ × 3
- Common: 2² = 4 → GCF = 4

#### 8. 54, 12
- 54 = 2 × 3³
- 12 = 2² × 3
- Common: 2 × 3 = 6 → GCF = 6

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Column 2:

#### 1. 56, 63
- 56 = 2³ × 7
- 63 = 3² × 7
- Common: 7 → GCF = 7

#### 2. 88, 66
- 88 = 2³ × 11
- 66 = 2 × 3 × 11
- Common: 2 × 11 = 22 → GCF = 22

#### 3. 30, 12
- 30 = 2 × 3 × 5
- 12 = 2² × 3
- Common: 2 × 3 = 6 → GCF = 6

#### 4. 36, 16
- 36 = 2² × 3²
- 16 = 2⁴
- Common: 2² = 4 → GCF = 4

#### 5. 9, 45
- 9 = 3²
- 45 = 3² × 5
- Common: 3² = 9 → GCF = 9

#### 6. 18, 54
- 18 = 2 × 3²
- 54 = 2 × 3³
- Common: 2 × 3² = 18 → GCF = 18

#### 7. 20, 30
- 20 = 2² × 5
- 30 = 2 × 3 × 5
- Common: 2 × 5 = 10 → GCF = 10

#### 8. 48, 12
- 48 = 2⁴ × 3
- 12 = 2² × 3
- Common: 2² × 3 = 12 → GCF = 12

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Column 3:

#### 1. 42, 63
- 42 = 2 × 3 × 7
- 63 = 3² × 7
- Common: 3 × 7 = 21 → GCF = 21

#### 2. 88, 55
- 88 = 2³ × 11
- 55 = 5 × 11
- Common: 11 → GCF = 11

#### 3. 30, 60
- 30 = 2 × 3 × 5
- 60 = 2² × 3 × 5
- Common: 2 × 3 × 5 = 30 → GCF = 30

#### 4. 80, 16
- 80 = 2⁴ × 5
- 16 = 2⁴
- Common: 2⁴ = 16 → GCF = 16

#### 5. 75, 45
- 75 = 3 × 5²
- 45 = 3² × 5
- Common: 3 × 5 = 15 → GCF = 15

#### 6. 81, 54
- 81 = 3⁴
- 54 = 2 × 3³
- Common: 3³ = 27 → GCF = 27

#### 7. 90, 30
- 90 = 2 × 3² × 5
- 30 = 2 × 3 × 5
- Common: 2 × 3 × 5 = 30 → GCF = 30

#### 8. 48, 108
- 48 = 2⁴ × 3
- 108 = 2² × 3³
- Common: 2² × 3 = 4 × 3 = 12 → GCF = 12

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✔ Final Answers:

#### Column 1:
1. 27, 63 → 9
2. 77, 66 → 11
3. 10, 12 → 2
4. 20, 16 → 4
5. 9, 21 → 3
6. 18, 27 → 9
7. 20, 24 → 4
8. 54, 12 → 6

#### Column 2:
1. 56, 63 → 7
2. 88, 66 → 22
3. 30, 12 → 6
4. 36, 16 → 4
5. 9, 45 → 9
6. 18, 54 → 18
7. 20, 30 → 10
8. 48, 12 → 12

#### Column 3:
1. 42, 63 → 21
2. 88, 55 → 11
3. 30, 60 → 30
4. 80, 16 → 16
5. 75, 45 → 15
6. 81, 54 → 27
7. 90, 30 → 30
8. 48, 108 → 12

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Let me know if you'd like a visual explanation or method (like Euclidean algorithm) for any!