 Factorization of large integers is believed to be a computationally very difficult problem, and the security of many widely used cryptographic protocols is based upon its infeasibility.Another definition of the GCD is helpful in advanced mathematics, particularly ring theory.The greatest common divisor "g"  of two nonzero numbers "a" and "b" is also their smallest positive integral linear combination, that is, the smallest positive number of the form "ua" + "vb" where "u" and "v" are integers.