Mr. Norton, the eminent numismatist decides to divide his coin collection amongst his four children.

• The oldest child gets 1/2 of the collection,
• The second oldest child gets 1/3 of the collection.
• The third oldest child gets 1/n of the collection, where n is a positive integer.
• The youngest gets the remaining 50 coins.

How many coins at most can there be in the collection?