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.

Question

UpStudy AI · Accepted Answer

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:**
$$ 3v^{3} $$
The greatest common factor is $$ 3v^{3} $$.

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.