To determine the greatest common factor (GCF) of the expression \(18j + 27\), we can break down each term into its prime factors.
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The term \(18j\) can be factored as: \[ 18j = 2 \times 3^2 \times j \]
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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: \[ \text{The GCF of } 18j + 27 \text{ is } 9. \]