Let T(λ) and V(λ) be two polynomial matrices having dimensions l x l and m x l respectively, with T(λ) regular and of degree n and V(λ) of degree at most n – 1. It has recently been shown that a necessary and sufficient condition for T and V to be relatively right prime is that a certain nlm x nl matrix R(T, V) have full rank. It is shown here that if T and V have a greatest common right divisor D(λ), then provided D is regular, its degree k is equal to n – (1/l) rank R. Furthermore, if R˜. denotes the matrix of the first (n – k) lm rows of R, then it is shown that the last (n – k) l columns of R˜ are linearly independent and that the coefficient matrices of D can be obtained by expressing the remaining columns of R˜ in terms of this basis.