Question

please find the gcf of 30m+12n

Answer 1

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.

1. **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 \(6\).

2. **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 \(6\).