Find the greatest common factor of $$ 6 w^{4} $$ and $$ 15 y^{2} $$.

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UpStudy AI · Accepted Answer

To find the greatest common factor (GCF) of the expressions $$ 6w^4 $$ and $$ 15y^2 $$, we start by determining the GCF of the numerical coefficients and the GCF of the variable parts separately.

1. **Finding the GCF of the coefficients:**
   - The coefficients are $$ 6 $$ and $$ 15 $$.
   - We can find the prime factorization of each:
     - $$ 6 = 2 \times 3 $$
     - $$ 15 = 3 \times 5 $$
   - The common prime factor is $$ 3 $$.
   - Therefore, the GCF of $$ 6 $$ and $$ 15 $$ is $$ 3 $$.

2. **Finding the GCF of the variable parts:**
   - The variable parts are $$ w^4 $$ and $$ y^2 $$.
   - Since $$ w $$ and $$ y $$ are different variables, they do not share any common factors.
   - Thus, the GCF of $$ w^4 $$ and $$ y^2 $$ is $$ 1 $$.

3. **Combining the results:**
   - The GCF of the coefficients is $$ 3 $$.
   - The GCF of the variable parts is $$ 1 $$.
   - Therefore, the overall GCF of $$ 6w^4 $$ and $$ 15y^2 $$ is:
     $$
     3 \times 1 = 3
     $$

Thus, the greatest common factor of $$ 6w^4 $$ and $$ 15y^2 $$ is $$\boxed{3}$$.
The GCF of $$ 6w^4 $$ and $$ 15y^2 $$ is 3.

Find the greatest common factor of and .

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