Find the greatest common divisor between $a$ and $b$ when $ 3a+5b=6$ As the tittle says, I need to find the greatest common divisor between $a$ and $b$ when $3a+5b=6$ and $(a,b) \neq 1$ and $(a,3)=1$.--prophetes.ai

Find the greatest common divisor between $a$ and $b$ when $ 3a+5b=6$ As the tittle says, I need to find the greatest common divisor between $a$ and $b$ when $3a+5b=6$ and $(a,b) \neq 1$ and $(a,3)=1$.

_Hint:_ Since $(a, b)$ divides the left hand side of $3a + 5b = 6$, it must divide the right hand side as well, so $(a, b) = 1, 2, 3$ or $6$. Now what does $(a, 3) = 1$ tell us about the possibilities?