text: and In other words, the GCD is unique up to the multiplication by an invertible constant.
  In the case of the integers, this indetermination has been settled by choosing, as the GCD, the unique one which is positive (there is another one, which is its opposite). With this convention, the GCD of two integers is also the greatest (for the usual ordering) common divisor. However, since there is no natural total order for polynomials over an integral domain, one cannot proceed in the same way here. For univariate polynomials over a field, one can additionally require the GCD to be monic (that is to have 1 as its coefficient of the highest degree), but in more general cases there is no general convention. Therefore, equalities like  or  are common abuses of notation which should be read " is a GCD of  and " and " and  have the same set of GCDs as  and ". In particular,  means that the invertible constants are the only common divisors. In this case, by analogy with the integer case, one says that  and  are .
  Properties
  As stated above, the GCD of two polynomials exists if the coefficients belong either to a field, the ring of the integers, or more generally to a unique factorization domain.