Are the numbers $0$ and $13$ coprime with each other?

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I couldn't find an answer on the internet but my script fails solving this. I have to know this because this is required to prove something else (it has to do with random numbers and their period).

I cannot say if they are coprime because I don't know if they are coprime because of the fact that division by $0$ doesn't work.

On the other hand I say they are not coprime because we don't get to $\text{gcd}(0,13)=1$.

But this is very confusing for me, please help!

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$gcd(a, b) = d \iff g |a \wedge g |b \Rightarrow g |d$

Notice that $x |0$ for any $x $ therefore

$gcd(a, 0) = a $ because $a |0 \wedge a |a $ and there cannot be a bigger integer that divides $a $. If $a \neq 1$, then 0 and $a $ are not coprime.