Fast divisibility tests (by 2,3,4,5,.., 16)?

Question

What are the fastest divisibility tests? Say, given a little-endian architecture and a 32-bit signed integer: how to calculate very fast that a number is divisible by 2,3,4,

Answer 1

Fast tests for divisibility depend heavily on the base in which the number is represented. In case when base is 2, I think you can only do "fast tests" for divisibility by powers of 2. A binary number is divisible by 2ⁿ iff the last n binary digits of that number are 0. For other tests I don't think you can generally find anything faster than %.