Question about relations between two numbers

Question

Is there is any relation between numbers' bits when one is divisible by another? What is the relation between the bits of 36 and the bit sequences of 9 or 4 or 12, or between 10 (1010) and 5 (101), or 21 (10101) and 7 (00111)?

Thanks. I am sorry if some sentence is not correct, but I hope you understand what I want.

Answer 1

I know this is not exactly what you're asking, but it may be helpful. There are many tricks for establishing binary number divisibility by manipulation of bits. For example a binary number is divisible by three if the sum of its even binary bits minus the sum of its odd binary bits all modulus 3 is zero. Here's a link discussing binary divisibility.