Interesting Multiples

For how many positive integers n where 1n1000 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?

 Details and Examples  \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 6×185=1110 6 \times 185 = 1110 which also satisfies the conditions

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