To find the greatest common factor (GCF) of the expression \(30m + 12n\), we can look for the GCF of the coefficients \(30\) and \(12\) first.
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Find the GCF of the coefficients:
- The factors of \(30\) are: \(1, 2, 3, 5, 6, 10, 15, 30\)
- The factors of \(12\) are: \(1, 2, 3, 4, 6, 12\)
The common factors of \(30\) and \(12\) are: \(1, 2, 3, 6\).
The greatest of these is \(6\).
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Factor out the GCF: Now that we know the GCF of the coefficients is \(6\), we can factor \(6\) out of the expression: \[ 30m + 12n = 6(5m + 2n) \]
The GCF of the expression \(30m + 12n\) is \(6\).