To find the greatest common factor (GCF) of the expression \(30m + 12n\), we need to determine the GCF of the coefficients of the terms (30 and 12).
- Find the GCF of 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 \(1, 2, 3, 6\). Therefore, the GCF of 30 and 12 is 6.
- Since the terms in the expression are \(30m\) and \(12n\), the GCF can be factored out as follows:
The GCF of the expression \(30m + 12n\) is \(6\).
Thus, the GCF is:
\[ \boxed{6} \]