The GCD of two numbers "a" and "b" is the product of the prime factors shared by the two numbers, where a same prime factor can be used multiple times, but only as long as the product of these factors divides both "a" and "b". For example, since 1386 can be factored into 2 × 3 × 3 × 7 × 11, and 3213 can be factored into 3 × 3 × 3 × 7 × 17, the greatest common divisor of 1386 and 3213 equals 63 = 3 × 3 × 7, the product of their shared prime factors. If two numbers have no prime factors in common, their greatest common divisor is 1 (obtained here as an instance of the empty product), in other words they are coprime. A key advantage of the Euclidean algorithm is that it can find the GCD efficiently without having to compute the prime factors. 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.