 Gauss mentioned the algorithm in his "Disquisitiones Arithmeticae" (published 1801), but only as a method for continued fractions.Peter Gustav Lejeune Dirichlet seems to have been the first to describe the Euclidean algorithm as the basis for much of number theory.Lejeune Dirichlet noted that many results of number theory, such as unique factorization, would hold true for any other system of numbers to which the Euclidean algorithm could be applied.