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:
[tex]y^4,y^8,y^9[/tex]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:
[tex]y^4[/tex]