'Separated' in the Bible

Then Lot chose him all the plain of Jordan; and Lot journeyed east: and they separated themselves the one from the other.

And the LORD said unto Abram, after that Lot was separated from him, Lift up now thine eyes, and look from the place where thou art northward, and southward, and eastward, and westward:

And the LORD said unto her, Two nations are in thy womb, and two manner of people shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger.