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Euclidean Division

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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Euclidean Division -

Tag(s) : Mathematics, Arithmetics

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# Euclidean Division

## Euclidean Division A/B

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.

### 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: 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