You can always find the GCF if you break the two numbers down to their prime factors. A fundamental theorem holds that each number has only one prime factorization.
For example, the prime factorization of 1680 is 24 357 and the prime factorization of 6048 is 25 33 7 .
The GCF of a pair of numbers is always the product of the prime factors they have in common.
Hope this helps,
Stephen La Rocque.