We describe an efficient algorithm for computing the associated equations appearing in the Beke-Schlesinger factorisar tion method for linear ordinary differential operators. This algorithm, which is based on elementary operations with sets of integers, can be easily implemented for operators of any order, produces several possible associated equations, of which only the simplest can be selected for solving, and often avoids the degenerate case, where the order of the associated equation is less than in the generic case. We conclude with some fast heuristics that can produce some factorisations while using only linear computations.