Mod

The whole number remainder of a number when it is divided by a given divisor (modulus). In Minitab, this function is represented by MOD (m, n) where m is the number and n is the divisor, and m and n are integers. For example, MOD (23, 10) = 3 because 23 divided by 10 results in a remainder of 3. In standard notation, this is expressed as 23 = 3 (mod 10).

Modular arithmetic, sometimes called "clock arithmetic," is a system that describes how numbers "wrap around" after they reach a certain value — the modulus. A standard clock can be considered modulo 12, where adding any multiple of 12 hours results in the same time position.

Modular arithmetic is important in number theory and can be used to simplify computations of extremely large numbers, because many numbers are equivalent in a given MOD. Modular arithmetic also plays an important role in abstract algebra, cryptography, computer science, and the visual and musical arts.

In Minitab, you can find the MOD of a number using the Calculator.