Task 1. A number was multiplied by the sum of its digits and the result was 2008. Find this number.

$[4$ points] (I. V. Yashchenko)
Answer: 251.

Solution: The desired number is a divisor of the number 2008. Let's factorize the number 2008 into prime factors: $2008=2 \cdot 2 \cdot 2 \cdot 251$. List all divisors of the number $2008: 1,2,4,8,251,502,1004,2008$. By finding the sum of the digits of each of them, we notice that the condition of the problem is only satisfied by the number $251(2008=251 \cdot(2+5+1))$.