Logic Problem: How to separate the real and counterfeit coins in the fewest number of turns?

There are 16 coins. An unknown number K of them are counterfeit and need to be separated. All of the coins look identical and feel identical, except that they are lettered A-P. Luckily, there is a machine that will accept any number of coins at once and return a “yes” is there is at least one counterfeit coin in that sample, and “no” otherwise. (all of the coins are returned)

The goal is to find a strategy that finds ALL counterfeit coins in the fewest number of turns (each use of the machine is one turn).

One strategy is to use the machine 16 times to test each coin one by one; however, if you test a large number of coins and get a “no” response, then you know that all of the coins are real and can save some turns.