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.

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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.

Answers to Questions

How to calculate the quotient of the euclidean division?

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

Example: Consider the division \( 43/21 = 2.047619...\), the quotient equals \( 2 \) (the integer part).

How to calculate the remainder of the euclidean division?

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

Example: Consider 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 make the remainder a positive value?

To get a positive remainder, subtract \( 1 \) to the quotient and add it to the negative remainder.

Example: If \( a = 15, b = 4 \), then ou can have \( q = 4, r = -1 \) (negative) because \( b \times q + r = 4 \times 4 - 1 = 15 = a \).

Example: Another possibility is to take \( q = ( 4 - 1 ) = 3 \) and then have \( r = 3 \) (positive) and \( b \times q + r = 4 \times 3 + 3 = 15 = a \)

Why the name Euclidean Division?

The name 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

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