 The extended Euclidean algorithm was published by the English mathematician Nicholas Saunderson, who attributed it to Roger Cotes as a method for computing continued fractions efficiently.In the 19th century, the Euclidean algorithm led to the development of new number systems, such as Gaussian integers and Eisenstein integers.In 1815, Carl Gauss used the Euclidean algorithm to demonstrate unique factorization of Gaussian integers, although his work was first published in 1832.