How old was Shem when he died?

According to Genesis 11:10-11, Shem was 600 years old when he died.

This part of Genesis has all the hallmarks of fiction, so we should not accept this as Shem's real age even if he was a real, historical person. Noah was 500 years old when he first became a father (Genesis 5:32) and the Flood happened when Noah was 600 (Genesis 7:11). Shem was exactly 100 years old when he became a father, and then lived to 600 years. Too many nice, round numbers.