Arithmetic : Properties of Integers and Numbers

Quotients and Remainders

Consider the following example. When 34 is divided by 6, the quotient is 5 and the remainder is 4 because 34 = 6 × 5 + 4.
In general, when integer m (dividend) is divided by a non-zero integer n (divisor), then there exist a unique integer q (quotient) and a unique integer r (remainder) such that m = n × q + r.
Note that m is divisible by n if and only if the remainder r is zero, i.e., m = n × q where q is an integer.
For example, 36 is divisible by 6 because the remainder is 0 when 36 is divided by 6.