Problem 703

【Answer】Solution: The unit digit of the natural number $N$ is 0, so it must have prime factors 5 and 2. To make $N$ the smallest, the number of 5s should be at least 1, and the other factors should preferably be 2 and 3, with the number of 2s not exceeding 2, and the rest preferably being 3;

Let this natural number $N=2^{1} \times 5^{1} \times 3^{a}$, according to the divisor sum theorem, we get:
$$\begin{aligned} (a+1) \times(1+1) \times(1+1) & =8, \\ (a+1) \times 2 \times 2 & =8, \\ a & =1 ; \end{aligned}$$

Therefore, the smallest $N$ is: $2 \times 3 \times 5=30$;
Answer: The smallest $N$ is 30.
The answer is: 30.