Question

Factor 54a+30b+12.
Write your answer as a product with a whole number greater than 1.

Answer 1

To factor the expression \(54a + 30b + 12\), we first need to find the greatest common factor (GCF) of the coefficients \(54\), \(30\), and \(12\).

1. The factors of \(54\) are \(1, 2, 3, 6, 9, 18, 27, 54\).
2. The factors of \(30\) are \(1, 2, 3, 5, 6, 10, 15, 30\).
3. The factors of \(12\) are \(1, 2, 3, 4, 6, 12\).

The common factors are \(1, 2, 3, 6\), and the greatest of these is \(6\).

Now we can factor out \(6\):

\[
54a + 30b + 12 = 6(9a + 5b + 2)
\]

Thus, the factored expression is:

\[
\boxed{6(9a + 5b + 2)}
\]