Question

finding greatest common factors for large numbers... any methods?

Answer 1

factor each number. take the product of the factors they have in common

Answer 2

by which i mean factor as the product of primes. so for example if one number is
\[2^2\times 3\times 7^3\] and the other is
\[2^3\times 3\times 5\times 7\] the greatest common factor is
\[2^2\times 3\times 7\]