text: and this factorization is unique up to the multiplication of the content by a unit of  and of the primitive part by the inverse of this unit.
  Gauss's lemma implies that the product of two primitive polynomials is primitive. It follows that
  and
  Relation between the GCD over R and over F
  The relations of the preceding section imply a strong relation between the GCD's in  and in . To avoid ambiguities, the notation "gcd" will be indexed, in the following, by the ring in which the GCD is computed.
  If  and  belong to , then
  If  and  belong to , then
  and
  Thus the computation of polynomial GCD's is essentially the same problem over  and over .
  For univariate polynomials over the rational numbers, one may think that Euclid's algorithm is a convenient method for computing the GCD. However, it involves simplifying a large number of fractions of integers, and the resulting algorithm is not efficient. For this reason, methods have been designed to modify Euclid's algorithm for working only with polynomials over the integers. They consist of replacing the Euclidean division, which introduces fractions, by a so-called pseudo-division, and replacing the remainder sequence of the Euclid's algorithm by so-called pseudo-remainder sequences (see below).
  Proof that GCD exists for multivariate polynomials