# Modular arithmetic

## Computation modulo a fixed integer / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Modular arithmetic?

Summarize this article for a 10 years old

In mathematics, **modular arithmetic** is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the **modulus**. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book *Disquisitiones Arithmeticae*, published in 1801.

A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in 7 + 8 = 15, but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic *modulo* 12. In terms of the definition below, 15 is *congruent* to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock.