Divisibility rule

Summary

A divisibility rule is a short method to decide whether a fixed integer $d$ divides an integer $n$. It uses the digits of $n$, and it does not need a full division. Most rules for base $10$ come from the congruences of the powers $10^k$ modulo $d$. For example, $10 \equiv 1 \pmod 3$, so $n$ and the sum of its digits have the same remainder modulo $3$.