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 ...

Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only ...