Factorize 1 236 519.
$\lceil \sqrt{1236519} \rceil = 1112$, and $1112^2 - 1236519 = 5^2$, and so $1236519 = 1112^2 0 5^2 = (1112+5)(1112-5) = 1117 \times 1107$.
We notice that the digits of 1107 sum to 9, and so is divisible by 9. In fact, we find it is divisible by 27, leaving prime 41. We also find the 1117 is prime, by testing up to $\sqrt{1117}$.
So the factorisation is $1236519 = 3^3 \times 41 \times 1117$.