2. (5 points) When dividing the numbers 312837 and 310650 by a certain three-digit natural number, the remainders were the same. Find this remainder.
Answer: 96

Solution. $312837-310650=2187=3^{7}$. The three-digit divisors of this number are also powers of three, i.e., $3^{6}=729,3^{5}=243$. By dividing these numbers by 729 and 243 with a remainder, we find that the remainder is always 96.