Floor Division Game

Henry and Derek are waiting on a room, eager to join the Snackdown 2016 Qualifier Round. They decide to pass the time by playing a game. In this game's setup, they write N positive integers on a blackboard. Then the players take turns, starting with Henry. In a turn, a player selects one of the integers, divides it by 2, 3, 4, 5 or 6, and then takes the floor to make it an integer again. If the