# Modulo | Mod Calculator – Free Online mod Calculator

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## What is Modulo / Mod Calculator?

Modulo is a math operation that finds the remainder when one number is divided by another. It is frequently abbreviated as a mod, or represented by the symbol %. Modular / mod arithmetic, sometimes called clock arithmetic, is a calculation that involves a number that resets itself to zero time a whole number greater than 1, which is mod, is reached. An example of a number is below.

For two integers a and b:

a mod b = result

Where a is the dividend, b is the divisor, (Mod)and result is the remainder.

## Who Created Modular Arithmetic?

According to Britannica, the concept of modular arithmetic has been used by ancient civilizations such as the Indians and Chinese. An example is the Chinese book Master Sun’s Mathematical Manual, which dates back from 300AD.

In particular, they occur in calendrical and astronomical problems since these involve cycles (Man-made or natural), but one also finds modular arithmetic is a purely mathematical problem.

### Modular / Mod Examples

15 mod 4 = 3, because 11 divides by 4 (thrice), with 3 remaining.

30 mod 6 = 0, because 30 divides by 5 (five times), with 0 remaining.

153 mod 7 = 6, because 153 divides by 7 (Twenty-one times), with 6 remaining.

## What is Real-World uses the Mod?

For practical applications, mod is very useful for dealing with time.

Since we have 24 hours in day, these is the principle behind the military time system, beginning at midnight with 0000 hours, and ending the hour at 11 PM with 2300 hours.