Question
Factor Algebraic Expressions Quick Check
Find the GCF of 42m — 28n.
A: 14
B: 84
C: 7
D: 2
Find the GCF of 42m — 28n.
A: 14
B: 84
C: 7
D: 2
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expression \(42m - 28n\), we can first find the GCF of the numerical coefficients, which are 42 and 28.
1. **Finding the GCF of 42 and 28:**
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- The factors of 28 are: 1, 2, 4, 7, 14, 28
- The common factors are: 1, 2, 7, 14
- The greatest common factor is 14.
2. **Checking if the variables (m and n) have any common factors:**
- The variables \(m\) and \(n\) are different, so they do not have any common factors.
Thus, the overall GCF of the expression \(42m - 28n\) is **14**.
The correct answer is **A: 14**.
1. **Finding the GCF of 42 and 28:**
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- The factors of 28 are: 1, 2, 4, 7, 14, 28
- The common factors are: 1, 2, 7, 14
- The greatest common factor is 14.
2. **Checking if the variables (m and n) have any common factors:**
- The variables \(m\) and \(n\) are different, so they do not have any common factors.
Thus, the overall GCF of the expression \(42m - 28n\) is **14**.
The correct answer is **A: 14**.