$($It$\text{'}$s a coincidence that $y=b$ here.$)$

My question is whether there's a connection between the number of divisions

that you carry out to compute $gcd(a,b)$ and the sign of the number $x.$ In the

example, there were seven divisions and the sign of $x($which was $-24)$ is negative.

In general, can you prove something about the relation between the number of

equations and the sign of $x?$