What is the quickest and most simple way of **integer factorization by hand**?

Question

I've searched for some algorithms but still wonder which method is best for human to calculate a not that big one such as: Calculate the factorization of 2345 and 3456

Note: Just for the examples, you will see it's not random number. Is there special method for such number?

Answer 1

In special cases (like these ones) you can use the difference of two squares.

3456 = 3600 - 144 = $60^2 - 12^2$ = (60 + 12)(60-12) = 72 * 48

2345 = 2601 - 256 = $51^2 - 16^2$ = (51 + 16)(51-16) = 67 * 35

From there it is straightforward to factor.