Question
Find the greatest common factor. \[ 2 j^{3}, 6 j^{3} \]
Ask by Wilson Ball. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor is \(2j^3\).
Solution
1. Write the two terms: \(2j^3\) and \(6j^3\).
2. Find the greatest common factor (GCF) of the numerical coefficients:
- The coefficients are \(2\) and \(6\).
- The GCF of \(2\) and \(6\) is \(2\).
3. Find the GCF of the variable part:
- Both terms have \(j^3\).
- The common variable factor is \(j^3\).
4. Multiply the GCF of the coefficients and the variable part:
\[
\text{GCF} = 2 \cdot j^3 = 2j^3
\]
Thus, the greatest common factor is \(2j^3\).
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Simplify this solution Bonus Knowledge
To find the greatest common factor (GCF) of \(2 j^{3}\) and \(6 j^{3}\), we start by breaking them down. The coefficients are 2 and 6. The factors of 2 are just 1 and 2, while the factors of 6 are 1, 2, 3, and 6. The greatest common factor among these coefficients is 2. Now, looking at the variable part, both terms have \(j^{3}\) in common. Therefore, we can combine these findings. The GCF is the product of the GCF of the coefficients and the common variable term, which gives us: \[ \text{GCF} = 2 j^{3} \] So, the greatest common factor of \(2 j^{3}\) and \(6 j^{3}\) is \(2 j^{3}\).
