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
