Question

Determine the GCF (greatest common factor) of the expression 42m−28n
.(1 point)
The GCF for 42m−28n
is

Answer 1

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

1. **Find the prime factors of 42 and 28:**
- \(42 = 2 \times 3 \times 7\)
- \(28 = 2^2 \times 7\)

2. **Identify the common prime factors:**
- The common prime factors are \(2\) and \(7\).

3. **Calculate the GCF:**
- The lowest exponent for each common prime factor:
- For \(2\): the minimum exponent is \(1\) (from \(42\)).
- For \(7\): the minimum exponent is \(1\) (from both).

So, the GCF is:
\[
2^1 \times 7^1 = 2 \times 7 = 14
\]

4. **Conclusion:**
The GCF of the coefficients in the expression \(42m - 28n\) is \(14\).

Therefore, the GCF for \(42m - 28n\) is \(\boxed{14}\).