The greatest common factor of a list of algebraic expressions with whole powers, is the combination of the lowest powers of each variable in the expression.
In the list:
![y^4,y^8,y^9](https://img.qammunity.org/2023/formulas/mathematics/college/t8qak8w8paxp1iz8cgft0c47hm7wkc9ghm.png)
There is one single variable: y. And the lowest power that it appears with is 4.
Therefore, the greatest common factor of y^4, y^8, y^9 is:
![y^4](https://img.qammunity.org/2023/formulas/mathematics/middle-school/yhiorndi23bj73zavqq7xqb7eicm1uzd7x.png)