...you think Khufu built it?
I'm more inclined to think that one of the Gods, likely Thoth built it.
"When Ra retired from the earth, he appointed Thoth and told him of his desire to create a Light-soul in the Duat and in the Land of the Caves, and it was over this region that the sun god appointed Thoth to rule.
During the late period of Egyptian history a cult of Thoth gained prominence, due to its main centre, Khnum (Hermopolis Magna), in Upper Egypt also becoming the capital.
Thoth's qualities also lead to him being identified by the Greeks with their closest matching god - Hermes, with whom Thoth was eventually combined, as Hermes Trismegistus."
Was Khufu around at the time as King?
Was the GP a tomb for a king?
Not it's original purpose.