The Euclidean algorithm works with numbers of any size. To find the greatest common divisor of 77 and 187 using the Euclidean algorithm involves the process of long division, which you might have ...

A. W. Goodman, W. M. Zaring, Euclid's Algorithm and the Least-Remainder Algorithm, The American Mathematical Monthly, Vol. 59, No. 3 (Mar., 1952), pp. 156-159 ...

We show that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann Hypothesis for ...