Fermat Factorisation

The Fermat factorisation is a method to find the factors of a large number.
It is useful when the factors are close to each other, however this method becomes inefficient if the factors are not close.

Steps

1) Start from $t = \ceil{\sqrt{n}}$
2) Try get an integer from $s = \sqrt{t^2 - n}$
3) Else, try get an integer from $s = \sqrt{(t+1)^2 - n}$
4) …
5) Two factors are $(t + s)(t - s)$

Once found, the factors are:
$a = t + s$
$b = t - s$

If you don't have a calculator

We can expand $(t+1)^2 - n = t^2-n + 2t+1$, and so therefore we can construct a table, and add the previous results to get the next result.