Tool to make an euclidean division automatically. Euclidean division is 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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Tool to make an euclidean division automatically. Euclidean division is 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.

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 $.

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

The name 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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