How to find the smallest number with just 0 and 1 which is divided by a given number?

Question

Every positive integer divide some number whose representation (base 10) contains only zeroes and ones.

One can prove that:

Consider the numbers 1, 11, 111,

Answer 1

My algorithm will be :-

1)Construct the sorted tree of of n possible numbers(say n initially is 10). So in this example it will contain 1,10,11,100,101,110,111....

2)Then loop over the list and perform on each no x%GivenNo, if its o its smallest possible no

3)Otherwise repeat step 3 with another 10 numbers