408. From the set of numbers

$$
\{2 ; 3 ; 9 ; 27 ; 81 ; 243 ; 567\}
$$

numbers $a, b, q$ and $r$ are chosen such that equation (1) is satisfied. Find the dividend, divisor, quotient, and remainder.
$\triangle$ Let's start with the dividend. It is not equal to 2, 3, or 9, since it is the largest of the four numbers. It is also not equal to 27, 81, or 243, as dividing each of these numbers by all preceding numbers results in a remainder of 0 or 1 (check this!), and the numbers 0 and 1 are not among the elements of the set. Therefore, the dividend is 567.

Now let's move to the divisor. It is different from the numbers $3, 9, 27$, and 81, since 567 is divisible by each of these numbers without a remainder. Thus, the divisor is either 2 or 243. But 2 is excluded, as 567 divided by 2 leaves a remainder of 1; the only remaining number is 243.

It remains to divide 567 by 243 with a remainder:

$$
567 = 243 \cdot 2 + 81.
$$

Answer: $567, 243, 2, 81$.