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

Modulo N Calculator - dCode

Tag(s) : Arithmetics, Mathematics

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

**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.

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():

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

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

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