To find the greatest common factor (GCF) of the expression \(42m - 28n\), we first need to find the GCF of the coefficients of the terms, which are 42 and 28.
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Find the prime factors of 42 and 28:
- \(42 = 2 \times 3 \times 7\)
- \(28 = 2^2 \times 7\)
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Identify the common prime factors:
- The common prime factors are \(2\) and \(7\).
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Calculate the GCF:
- The lowest exponent for each common prime factor:
- For \(2\): the minimum exponent is \(1\) (from \(42\)).
- For \(7\): the minimum exponent is \(1\) (from both).
So, the GCF is: \[ 2^1 \times 7^1 = 2 \times 7 = 14 \]
- The lowest exponent for each common prime factor:
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Conclusion: The GCF of the coefficients in the expression \(42m - 28n\) is \(14\).
Therefore, the GCF for \(42m - 28n\) is \(\boxed{14}\).