 An arbitrary PID has much the same "structural properties" of a Euclidean domain (or, indeed, even of the ring of integers), but when an explicit algorithm for Euclidean division is known, one may use Euclidean algorithm and extended Euclidean algorithm to compute greatest common divisors and Bézout's identity.In particular, the existence of efficient algorithms for Euclidean division of integers and of polynomials in one variable over a field is of basic importance in computer algebra.So, given an integral domain , it is often very useful to know that has a Euclidean function