Yashchenko I.v.

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

#
The sought number is a divisor of the number $2008=2^{3} \cdot 251$. Let's list all divisors of 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 for the number 251 $(2008=251 \cdot(2+5+1))$.

## Answer

251.