I believe the notation implies that M sub q has a factor of q. Obviously, if p divides M as well, then M has factors of p and q. What exactly is the question asking? Are you supposed to find p or M or q, or all of them? You will see this notation quite a bit when you are dealing with points in three-space and in dealing with augmented matrices.
"Given enough time, man can do anything with a bit of string and some Tinker toys." Bruce Bolden, Senior Instructor at the University of Idaho.