Remainder is the number that is "left over" from division. Even if a number \(n\) is not divisible by another number \(k\), it is still possible to divide \(n\) by \(k\), but with a remainder \(r\). Then, we can write \(n = qk +r\), where we always have \(0\leq r<k\). That is because we say that \(k\) goes into \(n\) \(q\) times, and a little bit is left. If that little bit was larger than \(k\), it could "go into" \(n\) once more. For example, a remainder of \(44\) in division by \(7\) is \(2\), because \(44 = 6 \times 7 + 2\).
The general rule is that a remainder of a sum, difference or a product of two remainders is equal to the remainder of a sum, difference or a product of the original numbers. What that means is if we want to find a remainder of a product of two numbers, we need to look at the individual remainders, multiply them, and then take a remainder. Let’s have a look on some examples: