Factor Algebraic Expressions Quick Check

Question

Find the GCF of 42m — 28n.
A: 14
B: 84
C: 7
D: 2

Answer 1

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.