Numbers are interesting, but some are inherently more interesting than others, by various criteria. Given a collection of numbers, you are to find the most interesting ones.
A number X is more interesting than another number Y if it has more attributes than Y. For the purposes of this problem, the attributes that are interesting are:
Note that 0 has no multiples other than itself, and 1 is not prime.
In addition to the above attributes, there are also those which depend on the other numbers in a given collection:
This makes for a total of thirteen possible attributes. Note that meeting the criteria for a particular attribute in multiple ways (1 is the factor of all other numbers, for example) still only counts as a single instance of an attribute.
Given a collection of numbers, you are to determine which numbers in that collection are most interesting.