The azeotropic behavior of a mixture can limit the feasible separations that are possible by both continuous and batch distillation. The azeotropes can create continuous and batch distillation boundaries and regions, and knowledge of these boundaries and regions is very important during the synthesis and design of distillation based separation systems. Infeasible designs can be screened out early in the design process, saving valuable time and resources. We propose an algorithm to find the basic distillation regions from which all of the continuous and batch distillation regions for an n-component system can be found, given all the azeotropes, their boiling point temperatures, and their node/saddle characteristics. A basic distillation region is a set of residue curves which all share the same unstable and stable node pair. Within each basic region, continuous and batch distillation regions can be determined. These regions give information about the types of feasible products one can obtain using either continuous or batch distillation. This algorithm can be applied to continuous columns and batch rectifiers, strippers, and middle vessel columns. The algorithm determines the boundaries and regions for all h-component systems before solving the (k + 1)-component systems. In this manner, we will show how to find the distillation boundaries and regions for any n-component system.