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 can divide a), denoted b|a. note that if b is 0, it is not called integer division.

properties of divisibility: (1) if a is divisible by b and c is any integer, then the product ac can also be divisible by b; (2) if a is divisible by both b and c at the same time, and b and c are relatively prime, then a must it is divisible by product bc and vice versa.