# euclidean division

## Calculus euclidean_division

The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.

### Function : euclidean_division

#### Summary :

The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.

euclidean_division online

#### Description :

The calculator with the euclidean_division function allows to do the euclidean division of polynomials online. As a calculator, euclidean_division also allows to do the euclidean division of two integers online.

# Euclidean division of two polynomials

A and B are two polynomials, to do euclidean division of A by B returns to find polynomials Q and R such that A=BQ+R with degree R< degree B. If R=0, we say that B divides A. This is sometimes called division shall descending powers.

To perform the euclidean division with the calculator, simply enter polynomials and to apply the euclidean_division function. Thus, for the euclidean division of polynomials such as the following : 1+x+x^2 et x, enter euclidean_division(x^2+x+1;x) or directly x^2+x+1;x, if the button euclidean_division already appears, the result {x^2+x+1=x*(1+x)+1} is returned. The quotient of the Euclidian division is 1+x and the remainder is equal to 1.

# Euclidean division of two integers

a and b are two integers, to do euclidean division of a by b returns to find integers q et r such that a = bq+r with r < b. If r = 0, we say that b divides a.

To perform the euclidean division with the calculator, simply enter the two integers and apply it to function euclidean_division. Thus, for the euclidean division of two integers such as the following : 19 et 3, you must enter euclidean_division(19;3) or directly 19;3, if the euclidean_division already appears, the result {19=3*6+1} is returned. The quotient is equal to 6 and the remainder of the euclidean division is 1.

The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.

#### Syntax :

• For polynomials divisions
• euclidean_division(polynomial;polynomial)
• or
• euclidean_division(polynomial/polynomial)
• For integers divisions
• euclidean_division(integer;integer)
• or
• euclidean_division(integer/integer)

#### Examples :

Calculate online with euclidean_division (euclidean division)
See also
• Degree of a polynomial : degree. The degree function calculates online the degree of a polynomial.
• Calculation of the discriminant online : discriminant. Calculator that allows the calculation of the discriminant of a quadratic equation online.
• Equation solver : equation_solver. The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.
• Euclidean division : euclidean_division. The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.
• Pythagorean theorem : pythagorean. The function makes it possible to verify by using the Pythagorean theorem knowing the lengths of the sides of a triangle that this is a right triangle. If the sides of the triangle depend on a variable, then the value of the variable is calculated so that the triangle is a right triangle.
• Valuation of a polynomial : valuation. The valuation function allows to calculate the valuation of a polynomial online.