Search for a tool
Modulo N Calculator

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

Results

Modulo N Calculator -

Tag(s) : Arithmetics

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Thanks to your feedback and relevant comments, dCode has developed the best 'Modulo N Calculator' tool, so feel free to write! Thank you!

Modulo N Calculator

Sponsored ads

Mod Calculator (A mod N)




Modular Exponentiation Calculator (a^b mod n)

Modular Inverse Calculator (a^-1 mod n)

Answers to Questions (FAQ)

What is a modulo in math?

The modulo is the name of a mathematical operation that, for 2 numbers $ a $ and $ b $, calculates the remainder $ r $ of the Euclidean division $ a \div b $. Mathematically the modular calculus is written $$ a \equiv r \mod{b} $$

Example: A heap of $ a = 123 $ marbles divides into $ b = 10 $ heaps of $ 12 $ marbles and there remains $ r = 3 $ marbles. So $ 123 $ modulo $ 10 $ is equal to $ 3 $, or $ 123 \equiv 3 \mod{10} $

The modulo operator is sometimes noted a%b=r with the percent sign %.

Modular calculations are often imaged with a circle, like on a clock where hour calculations are done modulo 12 (or 24) for hours and modulo 60 for minutes.

Example: It is 3:00 am, in 25 hours it will be 4:00 am, is equivalent to the calculation $ 3 + 25 \equiv 4 \mod{12} $ or even (3+25)%24=4
The minute hand is $ 15 $, in $ 90 $ minutes it will be $ 45 $, because $ 15 + 90 \equiv 45 \mod{60} $

How to calculate a Modulo A % N?

Method 1: Perform euclidean division and returns the remainder.

Example: Calculate $ A=123 $ modulo $ N=4 $, perform the Euclidean division of $ 123 / 4 = 30 \text{r} 4 $ as $ 123 = 30 \times 4 + 3 $ (the quotient is $ 30 $, and the remainder is $ 3 $). The modulo is the value of the remainder, so $ 123 \equiv 3 \pmod{4} $.

The negative modulo can be considered (rare), in this case $ 123 = 31 \times 4 - 1 $, so $ 123 \equiv -1 \pmod{4} $.

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 $ modulo $ 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 = 3 \pmod{4} $.

How to write a modulo?

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():

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

In spreadsheets like Excel, use MOD(A1;A2)

How to calculate a^b mod n?

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

How to calculate a^-1 mod n?

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

Where is the modulo in operators precedence order?

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

Source code

dCode retains ownership of the online 'Modulo N Calculator' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Modulo N Calculator' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Modulo N Calculator' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Modulo N Calculator' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Modulo N Calculator' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/modulo-n-calculator
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback