Problem 10.1. The smallest divisor of a number, different from 1, will be called minimal. The largest divisor of a number, different from the number itself, will be called maximal. Find a four-digit number for which the maximal divisor is 49 times greater than the minimal one. It is sufficient to provide an example of one such number.
Answer: 1225 or 2401.

Solution. Note that any divisor $d$ of a number $n$ corresponds to a divisor $n / d$, and the smaller $d$ is, the larger $n / d$ is, and this is a one-to-one correspondence of divisors with themselves.

Let $n$ be our four-digit number, and $p$ be its smallest divisor. Then the largest divisor of the number $n$ is $n / p$. In addition, it is not difficult to understand that $p$ is a prime number (otherwise, $n$ would have a divisor smaller than $p$ but greater than 1).

Let's write down the condition of the problem:

$$
\frac{n}{p}: p=49
$$

Multiplying by the denominators, we get $n=49 p^{2}$. This means that $n$ is divisible by 7, and then $p$ is a prime number not exceeding 7.

There are four prime numbers not exceeding 7 - these are $2, 3, 5$ and 7; but $n$ will be a four-digit number only when $p$ is equal to 5 or 7.