Modulo N Calculator

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.