I know that sheafification functor from the category of abelian presheaves on $C$ to the category of abelian sheaves on $C$. Here, $C$ is a category with Grothendieck pretopology.

My question is:

How about the sheafification functor from the category of presheaves of "sets" on $C$ to the category of sheaves of "sets" on $C$?

Is this an exact functor? (i.e. preserving finite limits and finite colimits?)

If so, how can one prove it?

In fact, I want to know whether sheafification functor preserves cartesian products or not.

Please give me any advice.