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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

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## Mod Calculator 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.

Example: Calculate $$A=123 \mod N=4$$, perform the Euclidean division of $$123 / 4$$ : $$123 = 30 \times 4 + 3$$ (the quotient is $$30$$, and the remainder is $$3$$). The modulo is the value of the remainder, so $$123 % 4 \equiv 3$$.

The negative modulo can be considered (rare), in this case $$123 = 31 \times 4 - 1$$, so $$123 % 4 \equiv -1$$.

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.

Example: Calculate $$A=123 \mod N=4$$, make the division: $$123/4 = 30.75$$. Keep the integer part $$30$$, and multiply by $$N=4$$, $$30 \times 4=120$$. 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, write it using the $$\equiv$$ congruence symbol and the keyword mod :

$$123 \ equiv 3 \mod 10$$

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

$$123 \% 10 = 3$$

On calculators, it is often implemented with the function 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.