Sum of factors of a huge number. I recently appeared in a math olympiad and it had this one question which had me stumped. This was a few weeks back and I have been looking for a way to find its answer ever since, but with no success. Searched the internet for the solution, but couldn't find any on it too! Anyway, here's how the question goes:
The value of $2^{96} - 3^{16}$ has two factors between 60 and 70. What is the sum of these two factors?
BTW, I should add that I did use wolframalpha to actually find the answer so I am more interested in knowing how to work it out manually than just knowing the answer. Any feedback would be appreciated.
Thanks!

Using $a^2-b^2 = (a+b)(a-b)$
\begin{align*}
2^{96}-3^{16}
={} &
(2^{48}+3^8)(2^{48}-3^8)
\\
={} &
(2^{48}+3^8)(2^{24}+3^4)(2^{24}-3^4)
\\
={} &
(2^{48}+3^8)(2^{24}+3^4)(2^{12}+3^2)(2^{12}-3^2)
\\
={} &
(2^{48}+3^8)(2^{24}+3^4)(2^{12}+3^2)(2^6+3)(2^6-3)
\end{align*}
and $2^6+3=67$, $2^6-3=61$, ...
