Pick any positive integer, for example your phone number. There is always another number that, multiplied by it, gives a result written only with the digits 0 and 1.
If your number ends in 1, 3, 7 or 9, you can even get a result made of nothing but 1s (a repunit).
Why it works. Take the numbers 1, 11, 111, … and look at their remainders modulo n. There are only n possible remainders, so two of them must repeat (pigeonhole). Subtract the two numbers and you get a multiple of n that looks like 111…1000…0. When n shares no factor with 10, the zeros are not needed and you get pure 111…1.