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 $t_0, t_1, t_2, \cdots$ be a sequence of elements of a field $F$. We give a continued fraction algorithm for $t_0x + t_1x^2 + t_2x^3 + \cdots$. If our sequence ...