A factory method can be static, but it isn't a "constructor". Ok, it constructs objects, but "constructor" refers to a special kind of method in a class that is for creating an instance of that class. It must have the same name as the class and not return anything (not even void). An official constructor cannot be declared static.
A factory method (as in the Facotry
Pattern (GoF)) will return different objects depending on what data it receives. But it is not an official "constructor", it is a method - which can be static.
I hope this helps.