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Find the GCF of 42m−28n .(1 point)

Responses

84
84

7
7

14
14

2

1 answer

To find the greatest common factor (GCF) of the expression \(42m - 28n\), we first look for the GCF of the numerical coefficients.

The coefficients are 42 and 28.

  1. Find the prime factorization of 42:
    \(42 = 2 \times 3 \times 7\)

  2. Find the prime factorization of 28:
    \(28 = 2^2 \times 7\)

Now, we identify the common prime factors:

  • The number 2 appears in both factorizations (the lowest power is \(2^1\)).
  • The number 7 also appears in both factorizations.

Next, we take the product of the lowest powers of the common prime factors:

\[ GCF = 2^1 \times 7^1 = 2 \times 7 = 14 \]

Now, putting it into the expression, we can factor out the GCF:

\[ 42m - 28n = 14(3m - 2n) \]

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

The correct response is 14.