Question
Find the greatest common factor. \( 3,6 k^{3} \) Write your answer as a constant times a product of single variables raised to exponents.
Ask by Goodwin Elliott. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The greatest common factor is \( 3 \).
Solution
To find the greatest common factor (GCF) of the terms \( 3 \) and \( 6k^{3} \), follow these steps:
1. **Factor Each Term:**
- \( 3 \) is a prime number, so its only factors are \( 1 \) and \( 3 \).
- \( 6k^{3} \) can be factored into its prime components: \( 6k^{3} = 2 \times 3 \times k^{3} \).
2. **Identify Common Factors:**
- The common factor between \( 3 \) and \( 6k^{3} \) is \( 3 \).
3. **Express the GCF:**
- Since there are no common variables with positive exponents in both terms, the GCF is simply the constant \( 3 \).
**Final Answer:**
\[ 3 \]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the greatest common factor (GCF) of the terms \(3\) and \(6k^3\), we start by identifying the common factors of the coefficients and the variable parts. The GCF of \(3\) and \(6\) is \(3\) since \(3\) divides both numbers. For the variable \(k\), it appears only in the second term, so it does not contribute to the GCF. Therefore, the GCF is \(3\). So, the greatest common factor is \(3\).
