For all positive integers $n$, $14^{6n} - 11^{6n}$ is divisible by ?
This question is followed with four options:
$1)157\quad\quad 2) 163\quad\quad 3) 225\quad\quad \quad 4) \text{All of these}$
I don't know how to do this in a "fast" way manually,what I did is used computer and factorized $14^6-11^6$ which gives $5757975=157\times 163 \times 225$ but surely this is not what I am supposed to do during exams as it will be too tedious even if I check for divisibility of the three numbers manually using the options but does computing $14^6-11^6$ and then checking for divisibility is the best option for solving this problem (manually/using pencil and paper)?