A polynomial in "n" variables may be considered as a univariate polynomial over the ring of polynomials in ("n" − 1) variables. Thus a recursion on the number of variables shows that if GCDs exist and may be computed in "R", then they exist and may be computed in every multivariate polynomial ring over "R". In particular, if "R" is either the ring of the integers or a field, then GCDs exist in "R"["x"1..., "xn"], and what precedes provides an algorithm to compute them.