If an integer a is divided by a non-zero integer b, the quotient is an integer and the remainder is zero, we say that a is divisible by b (or b is divisible by a), written as b|a. Note that b is not divisible if it is 0.

Divisibility properties: (1) If a is divisible by b, and c is an arbitrary integer, then the product ac is also divisible by b; (2) If a is divisible by both b and c, and b and c are coprime, then a must be divisible by the product bc, and vice versa.