Find the GCF of 42m−28n

Question

.(1 point)
Responses

7
7

84
84

14
14

2
2

Answer 1

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we can start by finding the GCF of the coefficients (42 and 28).

1. Factor the coefficients:

   • The prime factorization of 42 is \(2 \times 3 \times 7\).
   • The prime factorization of 28 is \(2^2 \times 7\).

2. Identify the common factors:

   • The common factors of 42 and 28 are \(2\) and \(7\).

3. Calculate the GCF:

   • The GCF is the product of the lowest powers of the common prime factors:
     • For \(2\), the lowest power is \(2^1\).
     • For \(7\), the lowest power is \(7^1\).

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

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