The problem asks to find the greatest common factor (GCF) for the given list of terms: $y^4$, $y^3$, and $y^6$.

To find the GCF of powers of the same variable, we need to identify the smallest exponent among the terms. In this case, the exponents of $y$ are:

• $y^4$ has an exponent of 4,
• $y^3$ has an exponent of 3,
• $y^6$ has an exponent of 6.

The smallest exponent is 3, so the GCF is $y^3$, not just $y$ (which would be $y^1$).

It looks like the given answer in the screenshot is $y$, but the correct GCF should be $y^3$.

Would you like more details or further clarification on this?

Here are 5 related questions to deepen your understanding:

1. How do you find the GCF of more complex algebraic terms involving multiple variables?
2. What happens if one of the terms has a coefficient (e.g., $2y^3$)? How does that affect the GCF?
3. How would you find the GCF of three polynomials?
4. What is the GCF of terms that involve negative exponents, like $y^{-2}, y^3, y^5$?
5. Can you explain why the smallest exponent determines the GCF?

Tip: When finding the GCF for powers of the same variable, always pick the variable with the smallest exponent as the common factor!