If the key consists of only digits thats bad to begin with because the number of permutations is rather small.
I woud say 'comparitively small'...
16-digits just numeric would be huge!
The combination math is:
nCr = n! / (r!(n - r)!)
(! = factorial)
where r=16
and n=10
However, with things like Credit Cards, there are other qualities (which can narrow down the search) for instance, if you total all the 16 digits, the sum would be a multiple of 7. (I think this was specific to visa and has now been made obsolete) also, the first set of 4 digits would be a control numebr for the issuing finance company, so the ACTUAL code would only be 12 digits.