Alocal reader's club has a set of 12 hardback books, a set of 18 paperbacks, and a set of 36 magazines. each set can be divided equally among the club members. what is the greatest possible number of club members?

The greatest possible number of club members is the greatest common factor of 12, 18, 36 since all of these quantities of books have to be distributed evenly: 

The factors of 12 are 1, 2, 3, 4, 6, 12 
The factors of 18 are 1, 2, 3, 6, 9, 18 
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

The greatest common factor for this three numbers is 6.
As a result, the greatest possible number of club members is 6.