The product of two natural numbers, neither of which is divisible by 10, is 1000. Find their sum.

#
Since $1000 = 5^3 \cdot 2^3$, each of the numbers in their prime factorization can only contain twos and fives. At the same time, both of these factors cannot be present in the factorization of one number, otherwise it would be divisible by 10.

Therefore, one of the numbers is $5^3$, and the other is $2^3$, and their sum is $5^3 + 2^3 = 125 + 8 = 133$.

## Answer

133.