To find the greatest common factor (GCF) of the expression \(42m - 28n\), we need to determine the GCF of the coefficients \(42\) and \(28\).
-
Find the factors of \(42\):
- \(42 = 2 \times 3 \times 7\)
-
Find the factors of \(28\):
- \(28 = 2^2 \times 7\)
-
Identify the common factors:
- Both \(42\) and \(28\) have \(2\) and \(7\) as common factors.
-
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, \(GCF = 2^1 \times 7^1 = 2 \times 7 = 14\).
- The lowest powers of the common prime factors:
Thus, the GCF of \(42m - 28n\) is \(14\).
Final answer: 14