Question
Find the greatest common factor. \( 9 v^{3}, 6 v^{3} \) Write your answer as a constant times a product of single variables raised to exponents.
Ask by Mullins Curry. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The greatest common factor is \( 3v^{3} \).
Solution
To find the greatest common factor (GCF) of the terms \( 9v^{3} \) and \( 6v^{3} \), follow these steps:
1. **Factor the Constants:**
- \( 9 = 3^2 \)
- \( 6 = 2 \times 3 \)
2. **Identify the GCF of the Constants:**
- The common prime factor is \( 3 \).
- So, the GCF of the constants is \( 3 \).
3. **Identify the GCF of the Variable Parts:**
- Both terms have \( v^3 \).
- So, the GCF of the variables is \( v^3 \).
4. **Combine the GCFs:**
- Multiply the GCF of the constants by the GCF of the variables.
- \( \text{GCF} = 3 \times v^3 = 3v^3 \)
**Final Answer:**
\[ 3v^{3} \]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the greatest common factor (GCF) of the terms \(9v^{3}\) and \(6v^{3}\), we start with the numerical coefficients. The GCF of 9 and 6 is 3, as it is the largest number that divides both coefficients. Next, we look at the variable part, \(v^{3}\). Since both terms share the same variable raised to the same power, we can take \(v^{3}\) as it is. Thus, the GCF of \(9v^{3}\) and \(6v^{3}\) is: \[ 3v^{3} \] Now you have the GCF nicely packaged as a constant times a product of variables!
