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.

Euclidean Division - dCode

Tag(s) : Arithmetics

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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 $.

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

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

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

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 $

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`

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

The name * euclidean division* comes from Euclid, a mathematician.

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

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- Long Division A/B
- Decimal Division
- Division Solver
- How to calculate the quotient of the euclidean division?
- How to calculate the remainder of the euclidean division?
- How to find the dividend of the euclidean division?
- How to find the divisor of the euclidean division?
- How to find the quotient of the euclidean division?
- How to make the remainder a positive value?
- How to calculate a division with a decimal number?
- What is the difference between decimal division and Euclidean division?
- What is a modulo calculation?
- Why the name Euclidean Division?
- What are the limits of this software?

division,long,euclidean,quotient,remainder,integer,euclide,dividend,divisor,modulo,algorithm,slice,calculator

Source : https://www.dcode.fr/euclidean-division

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