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

Here's a brute force version in Raku:

say (1..Inf).map( *.base(2) ).first( * %% $n );

The code generates a lazy (potentially infinite) sequence of candidate numbers and then searches for the first element that's divisible by n.

Being brute force it's not exceptionally fast, but the code is striking in its simplicity and expressiveness, as it is typical for Raku.