To find the Greatest Common Factor (GCF) of the expression \(42M - 28N\), we need to identify the GCF of the coefficients of the terms.
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Identify the coefficients: The coefficients of the terms \(42M\) and \(28N\) are \(42\) and \(28\), respectively.
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Find the GCF of the coefficients:
- The prime factorization of \(42\) is: \[ 42 = 2 \times 3 \times 7 \]
- The prime factorization of \(28\) is: \[ 28 = 2^2 \times 7 \]
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Identify the common factors:
- The common factors from the factorizations are \(2\) and \(7\).
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Multiply the smallest powers of the common prime factors:
- For \(2\), the smallest power is \(2^1\).
- For \(7\), the smallest power is \(7^1\).
- Therefore, the GCF is: \[ 2^1 \times 7^1 = 2 \times 7 = 14 \]
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Factor out the GCF from the expression:
- The GCF of the original expression \(42M - 28N\) is \(14\).
- We can rewrite the expression by factoring out the GCF: \[ 42M - 28N = 14(3M - 2N) \]
Thus, the GCF of the expression \(42M - 28N\) is \(14\).