Greatest common Divisor of negative numbers To find gcd of negative numbers we can convert it to positive number and then find out the gcd. Will it make any difference?

No. 
If $\langle a,b\rangle\in\mathbb Z\times\mathbb Z-\{\langle0,0\rangle\}$ then $\gcd\left(a,b\right)$
can be defined as the smallest positive element of set $\left\{ ra+sb\mid r,s\in\mathbb{Z}\right\} $.
Note that this set remains the same if $a$ is replaced by $-a$ and/or
$b$ is replaced by $-b$.
