Determine the prime decomposition of
$$ 8^8 − 1 = 16 777 215 $$
We have
$$ \begin{align} 16 777 215 & = (8^4-1)(8^4+1) \\ \\ & = (8^2-1)(8^2+1) \times 4097 \\ \\ & = 63 \times 65 \times 4097 \end{align} $$
We can factorise these separately
$ 63 = 3^2 \times 7 $
$ 65 = 5 \times 13 $
$ 4097 = 17 \times 241 $
And so
$$ 8^8 -1 = 3^2 \times 5 \times 7 \times 13 \times 17 \times 241 $$