 The matrix method is as efficient as the equivalent recursion, with two multiplications and two additions per step of the Euclidean algorithm.Bézout's identity is essential to many applications of Euclid's algorithm, such as demonstrating the unique factorization of numbers into prime factors.To illustrate this, suppose that a number "L" can be written as a product of two factors "u" and "v", that is, "L" = "uv".