To find the greatest common factor (GCF) of the expression \(30m + 12n\), we first need to find the GCF of the coefficients and then factor out any common variables.
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Find the GCF of the coefficients:
- The coefficients are 30 and 12.
- 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 are \(1, 2, 3, 6\).
- The greatest common factor is \(6\).
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Check for common variables:
- There are no common variables in \(30m\) and \(12n\) (one has \(m\) and the other has \(n\)).
Thus, the GCF of the expression \(30m + 12n\) is \(6\).
So, you can factor the expression as:
\[ 6(5m + 2n) \]
Final answer: The GCF of \(30m + 12n\) is \(6\).