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

You can replace division by a non-power-of-two constant by a multiplication, essentially multiplying by the reciprocal of your divisor. The details to get the exact result by this method are complicated.

Hacker's Delight discusses this at length in chapter 10 (unfortunately not available online).

From the quotient you can get the modulus by another multiplication and a subtraction.