Number of ultrafilters in the free Boolean algebra on countably many generators

Question

Let $A$ be the free Boolean algebra on denumerably many generators. How many ultrafilter does $A$ contain? How to prove it?

Answer 1

Hint: remember that an ultrafilter on $B$ is essentially the same as a boolean algebra morphism $B\to 2$. How can you characterize morphisms from a free algebra to $2$ ?