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Euclidean Division

Tool to make an euclidean division from the dividend and the divisor to get the quotient and the remainder.

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Euclidean Division -

Tag(s) : Arithmetics

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Euclidean Division

Long Division Algorithm A/B





Decimal Division

⮞ Go to: Division

Division Solver

Indicate 3 values among the 4 to find the last one





See also: Equation Solver

Answers to Questions (FAQ)

What is an euclidean division? (Definition)

Euclidean division is an arithmetical operation which associates to two (integer) numbers: the dividend and the divisor (not 0), two others numbers resulting from the division operation: the quotient and the remainder.

It can be calculated by hand with several steps (long division) or directly using a calculator.

How to calculate the quotient of the euclidean division?

Quotient $ q $ is the integer part of the division a/b (ignoring the resulting decimal part) 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 $$ r = a - q \times b $$. It represents what is left after the largest possible divisor multiple has been subtracted from the dividend (the remainder after the sharing).

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?

To find the dividend of Euclidean division, you can multiply the quotient by the divisor and add the remainder to it. The dividend $ a $ is then 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?

In mathematics, the remainder of Euclidean division can be positive or negative, but it is commonly agreed to take the positive remainder. If the remainder obtained is negative, you can add the divisor to it to make it positive by subtracting 1 from the quotient. To obtain a positive remainder, take as quotient $ q-1 $, the remainder is then increased 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

How to calculate if the divisor is greater than the dividend?

If the dividend is less than the divisor then the result of the division is 0 and the remainder is the dividend.

Example: 5/7 = 0 remainder 5

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 \mod 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.

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