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 ...

Stan Wagon, Editor's Corner: The Euclidean Algorithm Strikes Again, The American Mathematical Monthly, Vol. 97, No. 2 (Feb., 1990), pp. 125-129 ...

M. R. MURTY, KATHLEEN L. PETERSEN, THE EUCLIDEAN ALGORITHM FOR NUMBER FIELDS AND PRIMITIVE ROOTS, Proceedings of the American Mathematical Society, Vol. 141, No. 1 (JANUARY 2013), pp. 181-190 ...