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

Modulo N Calculator - dCode

Tag(s) : Arithmetics, Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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

dCode retains ownership of the source code of the script Modulo N Calculator online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Modulo N Calculator script for offline use, check contact page !

modulo,remainder,division,calculus,calculator,modular,euclide,euclidean,mod,fmod,modulus

Source : https://www.dcode.fr/modulo-n-calculator

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode