Division with remainder

You want to share 17 sweets fairly among 5 children. Each gets 3, and 2 stay in the bag. This leftover has a name: the remainder. It is not a mistake but real information, and you'll soon see how often it comes in handy.

Division with remainder

When a division does not come out evenly, you split it into two numbers: the whole-number result and the remainder. For 17 divided by 5 you write: 17 : 5 = 3 remainder 2. The number you divide by is called the divisor, here that is the 5. The remainder is always smaller than the divisor, otherwise you could have handed out one more portion.

Modulo: only the remainder counts

Sometimes you don't care about the result at all, only about the remainder. There is a word just for this: modulo, often shortened to mod. You say 17 mod 5 = 2, meaning exactly the remainder of 17 divided by 5. Programs compute this all the time, for example to shade every other row of a table: the row number mod 2 is either 0 or 1, and the colour follows from that.

Application: days of the week

A week has 7 days and repeats over and over. To find which day it is in 10 days, you compute 10 mod 7 = 3 and jump only 3 days ahead: Monday becomes Thursday. You can safely drop the 7 full days in between, since they lead back to the same weekday. Clock times with mod 12 or mod 24 work the same way, as does anything else that runs in a circle.