This paper describes the problem of factorization. It indicates the fundamental place of this problem in a number of purely mathematical and applied sciences. The structure of factorization classes methods is analyzed, the choice of the approach based on the elliptic curves theory is substantiated. The algorithm of elliptic curves is described and analyzed in detail. The paper describes the problem of the relationship between the generated curves number and the necessary boundary of the basic method of elliptic curves. The research of this problem are made by method software implementation. Results of this research are represented.