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Use any method to find the greatest common factor of each pair of numbers.

1. 12, 30
2. 4, 16
3. 9, 36
4. 35, 63
5. 42, 56
6. 54, 81

Sagot :

GinnyAnsweridn
Certainly! Let's find the greatest common factor (GCF) for each pair of numbers step-by-step.

### 1. Finding the GCF of 12 and 30

First, let's list the factors of each number:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Next, identify the common factors:
- Common factors of 12 and 30: 1, 2, 3, 6

The greatest common factor is the largest common factor:
- GCF of 12 and 30: 6

### 2. Finding the GCF of 4 and 16

List the factors of each number:
- Factors of 4: 1, 2, 4
- Factors of 16: 1, 2, 4, 8, 16

Identify the common factors:
- Common factors of 4 and 16: 1, 2, 4

The greatest common factor is:
- GCF of 4 and 16: 4

### 3. Finding the GCF of 9 and 36

List the factors of each number:
- Factors of 9: 1, 3, 9
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Identify the common factors:
- Common factors of 9 and 36: 1, 3, 9

The greatest common factor is:
- GCF of 9 and 36: 9

### 4. Finding the GCF of 35 and 63

List the factors of each number:
- Factors of 35: 1, 5, 7, 35
- Factors of 63: 1, 3, 7, 9, 21, 63

Identify the common factors:
- Common factors of 35 and 63: 1, 7

The greatest common factor is:
- GCF of 35 and 63: 7

### 5. Finding the GCF of 42 and 56

List the factors of each number:
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Identify the common factors:
- Common factors of 42 and 56: 1, 2, 7, 14

The greatest common factor is:
- GCF of 42 and 56: 14

### 6. Finding the GCF of 54 and 81

List the factors of each number:
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 81: 1, 3, 9, 27, 81

Identify the common factors:
- Common factors of 54 and 81: 1, 3, 9, 27

The greatest common factor is:
- GCF of 54 and 81: 27

### Summary of Results
Based on our step-by-step calculations, the greatest common factors for each pair of numbers are:
1. GCF of 12 and 30: 6
2. GCF of 4 and 16: 4
3. GCF of 9 and 36: 9
4. GCF of 35 and 63: 7
5. GCF of 42 and 56: 14
6. GCF of 54 and 81: 27
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