In this note divisors

of a given polynomial matrix

are discussed. The note deals with the following problems: extraction of a greatest right (left) divisor of

, computation for a given state-space system

a state-space feedback making the system

maximally or appropriately observable, and determination for a given system

a disturbance rejection feedback

. The developed methods are very simple from a computational point of view and can be easily implemented in the software via existing computer library procedures.