+506 The exponent of the prime factorization of the gcd of the 2 numbers will be the biggest power of that prime number that divides into both of the 2 giant numbers. Knowing that here is the prime factorization of the greatest common divisor of the 2 numbers:
\(2^23^35^57^711^{11}13^717^519^323^2\)
Therefore \(\boxed{11}\) is the answer.
