There is a massive issue when these two are mixed up, mainly because they mean the complete opposite.
She stood apart of the crowd.
She stood a part of the crowd.
Both have very different meanings. “A part” means together and with, while “apart” means separate and away from. Thus they are very different in how they are used.
The piece was a part of the whole.
Rusty was a part of her mom and a part of her dad.
Rusty was apart from Seeley for the better part of a week during a move.