Which Colleges Require an EFC of Zero?

I have seen much speculation about this topic on other posts, but they are either from five years ago and are irrelevant or the only response was that Yale was the only one that required an EFC of zero. Since I didn’t rank Yale, that really doesn’t apply to me, but I’m especially curious about Wellesley. It’s my dream school and assuming I’d match because of academic/extracurricular/test score reasons alone, will an EFC of $8k or so (I’m assuming, I don’t actually know what it is) hurt me? Which other schools require an EFC of zero? Any help is appreciated!