To find the greatest common factor (GCF) of the terms \(30m\) and \(12n\), we first look at the coefficients of each term:
- The coefficients are \(30\) and \(12\).
- We need to 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: \(1, 2, 3, 6\)
The greatest of these is \(6\).
Now, since the two terms \(30m\) and \(12n\) do not share any common variables (one has \(m\) and the other has \(n\)), the GCF is simply the GCF of the coefficients.
Thus, the GCF of \(30m + 12n\) is:
\[ \boxed{6} \]