Search for a tool
Euclidean Division

Tool to make an euclidean division, an arithmetical operation which associates to two numbers: the dividend and the divisor, two others numbers resulting from the division operation: the quotient and the remainder.

Results

Euclidean Division -

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 'Euclidean Division' tool, so feel free to write! Thank you!

Euclidean Division

Long Division A/B





Decimal Division

⮞ Go to: Division

Division Solver

Indicate 3 values amond the 4 to find the last one





See also: Equation Solver

Answers to Questions (FAQ)

How to calculate the quotient of the euclidean division?

Quotient $ q $ is the integer part of the division a/b where a is the dividend and b the divisor.

Example: In the division (or fraction) $ 43/21 = 2.047619\dots $, the quotient $ q = 2 $ (the integer part)

How to calculate the remainder of the euclidean division?

The remainder $ r $ is the result of $$ r = a - q \times b $$

Example: In the division $ 43/21 $, the quotient equals $ 2 $ and the remainder equals $ 43 - 21 \times 2 = 1 $, indeed $ 43 = 2 \times 21 + 1 $.

How to find the dividend of the euclidean division?

The dividend $ a $ is calculated from the other values $$ a = b \times q + r $$

How to find the divisor of the euclidean division?

The divisor $ b $ is calculated from the other values $$ b = \frac{a - r}{q} $$

How to find the quotient of the euclidean division?

The quotient $ q $ is calculated from the other values $$ q = \frac{a - r}{b} $$

How to make the remainder a positive value?

To get a positive remainder, take for quotient $ q-1 $, the remainder is then augmented by $ b $.

Example: If $ a = 15, b = 4 $, then is is possible to use $ q = 4, r = -1 $ (negative) because $ b \times q + r = 4 \times 4 - 1 = 15 = a $ but to get a positive remainder, take $ q = ( 4 - 1 ) = 3 $ and then have $ r = 3 $ (positive) and $ b \times q + r = 4 \times 3 + 3 = 15 = a $

How to calculate a division with a decimal number?

An Euclidean division is an entire division, it is not supposed to have decimal places.

However, if the divisor or the dividend has decimal places, it is possible to multiply by 10 the dividend and the divisor as many times as necessary to make it disappear.

Example: 1.2/3 is equivalent to having 12/30

What is the difference between decimal division and Euclidean division?

If the division stops at integer numbers (before the decimal point) then it is a Euclidean division, otherwise it is a decimal division.

What is a modulo calculation?

A modulo (mod) calculation is a division that is only interested in the remainder.

Example: $ 13 modulo 5 \equiv 3 $ (because $ 3 $ is the remainder of the division of $ 12 $ by $ 5 $)

Why the name Euclidean Division?

The name euclidean division comes from Euclid, a mathematician.

What are the limits of this software?

This software is not limited, it can calculated with any number, including big numbers with arbitrary precision

Source code

dCode retains ownership of the online "Euclidean Division" tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any "Euclidean Division" algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any "Euclidean Division" 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 "Euclidean Division" 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 'Euclidean Division' tool, so feel free to write! Thank you!


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