8.1. A natural number $n$ is called "good" if, when appended to the right of any natural number, the resulting number is divisible by $n$. Write down ten "good" numbers that are less than 1000. (It is sufficient to provide the answer.)
Answer: any 10 numbers from the set: $1,2,5,10,20,25,50,100,125,200,250,500$.

The answer can be obtained based on the following considerations. Appending a number p to the right is equivalent to multiplying the original number by $10^{p}$, where $p-$ is the number of digits in the number $n$, and adding the number p to the result. Since the original number can be any, the number $n$ will be "good" if and only if $10^{p}$ is divisible by p. Therefore, in the prime factorization of the number $n$, only the factors 2 and 5 can appear. Note that this is not sufficient; for example, the numbers 4 and 625 are not "good".

## Evaluation criteria:

+ at least 10 "good" numbers are correctly written, and no other numbers are in the answer

$\pm$ at least 10 "good" numbers are correctly written, but one or two numbers that are not "good" are also present in the answer

$\pm$ 8 or 9 "good" numbers are correctly written, and no other numbers are in the answer

干 at least 5-9 "good" numbers are correctly written, but one or two numbers that are not "good" are also present in the answer

- in all other cases
- the problem is not solved or solved incorrectly

The presence of any reasoning in the solution (including incorrect reasoning) does not affect the evaluation result.