We say one integer divides another if it does so evenly, that is with a remainder of zero (we sometimes say, "with no remainder," but that is not technically correct). More formally, mathematicians write:
If a and b are integers (with a not zero), we say a divides b if there is an integer c such that b = ac.We use this concept enough that it has its own symbols:
The integers that divide a are called the divisors of a.
You might want try your hand at proving the following basic properties which hold for all integers a, b. c and d: