3. Find all possible triples $(a, b, c)$ of positive integers with the following properties:

- $\operatorname{gcd}(a, b)=\operatorname{gcd}(a, c)=\operatorname{gcd}(b, c)=1$;
- $a$ is a divisor of $a+b+c$;
- $b$ is a divisor of $a+b+c$;
- $c$ is a divisor of $a+b+c$.

(Here $\operatorname{gcd}(x, y)$ is the greatest common divisor of $x$ and $y$.)