The authors show how the Euclidean algorithm fits into the behavioral framework of exact modeling and how it computes solutions of the scalar minimal partial realization problem. It turns out that the Euclidean algorithm can be considered as a special instance of Wolovich＇s procedure (1974) to achieve row reducedness for a given polynomial 2 x 2 matrix. The authors show in detail how this approach yields a parameterization of all minimal solutions in terms of polynomials that are sequentially produced by the Euclidean algorithm.