2. How many three-digit natural numbers have an even number of distinct natural divisors?
Answer: 878.

Solution: Note that only perfect squares have an odd number of divisors (for non-squares, divisors can be paired with their complements). There are 900 three-digit numbers in total. Among them, the perfect squares are $10^{2}, 11^{2}, \ldots, 31^{2}=961$ ( $32^{2}=1024-$ is a four-digit number). There are 22 of them, so the remaining 900-22 $=878$ are not squares.