Question

Find the GCF of 42m−28n
42
𝑚
−
28
𝑛
.(1 point)
Responses

2
2

14
14

7
7

84 ......

Answer 1

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we need to determine the GCF of the coefficients \(42\) and \(28\).

1. **Find the factors of \(42\)**:
- \(42 = 2 \times 3 \times 7\)

2. **Find the factors of \(28\)**:
- \(28 = 2^2 \times 7\)

3. **Identify the common factors**:
- Both \(42\) and \(28\) have \(2\) and \(7\) as common factors.

4. **Calculate the GCF**:
- The lowest powers of the common prime factors:
- For \(2\) the lowest power is \(2^1\) (from \(42\)).
- For \(7\) the lowest power is \(7^1\) (from both).
- So, \(GCF = 2^1 \times 7^1 = 2 \times 7 = 14\).

Thus, the GCF of \(42m - 28n\) is \(14\).

**Final answer: 14**