Tool to compute any modulo operation. Modulo is the name of the calculus of the remainder in the Euclidean division. The modulo calculator returns the rest of the integer division.

Modulo N Calculator - dCode

Tag(s) : Arithmetics

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**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 (from latin modulus) 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, write the % percentage symbol, easily accessible on a keyboard:

$$ 123 \% 10 = 3 $$

In functional programming, for integers there is often the function mod() and for floating point numbers, the function fmod().

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

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

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

In most computation languages, the modulo operator % has the same precedence as the multiplication or division operations.

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