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Modulo N Calculator

Tool to compute any modulo operation. Modulo is the name of the calculus of the remainder in the Euclidian division

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Modulo N Calculator -

Tag(s) : Arithmetics,Mathematics

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# Modulo N Calculator

## Modular Calculus a mod n

### Modular Exponentiation Calculus a^b mod n

Tool to compute any modulo operation. Modulo is the name of the calculus of the remainder in the Euclidian division

### How to calculate a Modulo A % N?

Method 1: Perform euclidean division and returns the remainder.

To calculate A=123 mod N=4, performe the Euclidean division of 123 by 4. You get 123 = 30 * 4 + 3 (the quotient is 30, and the remainder 3). The modulo is the value of the remainder. So 123 % 4 = 3.

You can also consider the negative modulo (rare), in this case 123 = 31 * 4 - 1. So you can write 123 % 4 = -1.

Dcode uses this method that applies to both large numbers, as point numbers for A. However, N be a natural number.

Method 2: Perform the integer division and calculate the value of the difference.

To calculate A=123 mod N=4, make the division: 123/4 = 30.75. Keep the integer part 30, and multiply by N=4, 30*4=120. The difference between 123 and 120 is 3. So 123% 4 = 3.

### How to write a modulo?

A modulo calculation can be written differently:

In Mathematics you can write it using the $$\equiv$$ congruence symbol and the keyword mod :

$$123 \ equiv 3 \mod 10$$

For computer and keyboard writings (on internet) you can write the % percentage symbol:

$$123 \% 10 = 3$$

On calculators, it is often implemented with the fonction mod():

$$\mod (123,10) = 3$$

### How to calculate a^b mod n?

This calculus is named modular exponentiation, use the dCode page dedicated to modular exponentiation.