One day at a family reunion we found a bunch of baseball cards in Grandpa's basement. Grandpa said we could split them among all the grandkids. There were 5040 cards in all, so each of us got a lot of cards. but then we remembered that the Paxtons, who had four of the grandchildren, hadn't arrived yet. That meant each of us present had to give up 42 cards, so that all the grandchildren would have the same number of cards.
How many grandchildren does Grandpa have?