# Modulo System

It is of common experience that a railway time table is fixed with the prevision of **24** hours in a day and night. When we say that a particular train is arriving at **15** hours, it implies that the train will arrive at **3** p.m. according to our watch. Thus all the timing starting from **12** to **23** hours correspond to one of **0, 1, 3,…,** **11 **O’clock, as indicated on watches. In other words, all integers from **12** to **23** are equivalent to one or the other of integers **0, 1, 2, 3, …, 11** with modulo **12.** Thus, the integers in question are divided into **12** classes.

In the manner described above the integer could be divided into **2** classes, or **5** classes or **m** (**m** being a positive integer) classes, and then we would have written **mod 2** or **mod 5** or **mod m**. This system of representing integers is called a modulo system.