459. Find all values of the greatest common divisor of the numbers $8 a+3$ and $5 a+2$, where $a$ is a natural number.
$\triangle$ Let's denote the greatest common divisor of these numbers by $d$. Then

$$
(8 a+3): d, \quad(5 a+2): d
$$

Multiply the sum $8 a+3$ by 5, and the sum $5 a+2$ by 8. We get:

$$
(40 a+15): d, \quad(40 a+16): d
$$

But two consecutive natural numbers $40 a+15$ and $40 a+16$ are coprime (see the statement of problem 454), therefore, $d=1$.

Answer: 1.