text: so the sequence will eventually reach a point at which
  and one has got the GCD:
  Example: finding the GCD of  and :
  Since  is the last nonzero remainder, it is a GCD of the original polynomials, and the monic GCD is  .
  In this example, it is not difficult to avoid introducing denominators by factoring out 12 before the second step. This can always be done by using pseudo-remainder sequences, but, without care, this may introduce very large integers during the computation. Therefore, for computer computation, other algorithms are used, that are described below.
  This method works only if one can test the equality to zero of the coefficients that occur during the computation. So, in practice, the coefficients must be integers, rational numbers, elements of a finite field, or must belong to some finitely generated field extension of one of the preceding fields. If the coefficients are floating-point numbers that represent real numbers that are known only approximately, then one must know the degree of the GCD for having a well defined computation result (that is a numerically stable result; in this cases other techniques may be used, usually based on singular value decomposition.
  Univariate polynomials with coefficients in a field