We must find the GCF of 16, 20, and 24. If we use this number of baskets, we can evenly divide each fruit into the baskets, but anything more will require a fractional amount of fruit.
The GCF of these numbers is four, because if each is divided by 4, we get 4, 5, and 8, which share no common factors other than one. Thus, four baskets at most can be made.