Find the GCF of 42m−28n

42
𝑚

28
𝑛
.(1 point)
Responses

2
2

14
14

7
7

84 ......

1 answer

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