An integer $d$ is a $\gcd$ of two non-zero integers $a$ and $b$, if
$d$ divides $a$ & $d$ divides $b$
'$c$ divides $a$ & $c$ divides $b$' implies '$c$ divides $d$' for any integer $c$.
If $e=gh$ where $e,g,h \in \{0,\pm1,\pm2,...\}, g\neq0$, then we say that $g$ divides $e$.
These are the definitions written in a maths book. The above definitions imply there are two gcd's, one a positive integer, another the negative of this positive integer. Am I correct? How can I find the gcd's? We find the hcf of │a│ and │b│ by division method, let it be $m \in \{1,2,\dots\}$. Then $m$ and $-m$ are the $\gcd$'s. Is this right?