Question

Determine the GCF (greatest common factor) for the expression 18j+27
.(1 point)
The GCF of 18j+27
is
.

Answer 1

To determine the greatest common factor (GCF) of the expression \(18j + 27\), we can break down each term into its prime factors.

1. The term \(18j\) can be factored as:
\[
18j = 2 \times 3^2 \times j
\]

2. The term \(27\) can be factored as:
\[
27 = 3^3
\]

Now, we can identify the common factors between the two terms. The only base common to both factorizations is \(3\).

- The minimum power of \(3\) in the factorization of \(18j\) is \(2\) (from \(3^2\)).
- In the factorization of \(27\), the power of \(3\) is \(3\).

Thus, the GCF of \(18j\) and \(27\) is:
\[
3^2 = 9
\]

Therefore, the GCF of the expression \(18j + 27\) is \(9\).

So, the final answer is:
\[
\text{The GCF of } 18j + 27 \text{ is } 9.
\]