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.

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 \( 123 % 4 = 3 \).

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 fonction mod():

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

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

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