# Interesting Multiples

For how many positive integers n where $$1 \le n \le 1000$$ does there exist some multiple of n which is a sequence of 1s followed by a sequence of 0s in base 10?

$$\textbf{ Details and Examples }$$

There must be at least one 1 at the beginning of the multiple and it must end in at least one 0

10 is such an n since it itself satisfies the conditions

6 is such an n since $$6 \times 185 = 1110$$ which also satisfies the conditions

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