The calculator allows to find online the quotient and the remainder in the euclidean division of two polynomials or two integers.

Quotient and Remainder Calculator

The calculator allows to do the euclidean division of polynomials online and 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 quotient and remainder calculator with the calculator, simply enter polynomials and to apply the euclidean_division function. Thus, for the quotient and remainder calculator 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 quotient and remainder calculator with the calculator, simply enter the two integers and apply it to function euclidean_division. Thus, for the quotient and remainder calculator 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.

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 :

• euclidean_division(`x^2+x+1;x`) returns `{x^2+x+1=x*(1+x)+1}`
• euclidean_division(`(x^2+x+1)/x`) returns `{x^2+x+1=x*(1+x)+1}`
• euclidean_division(`19;3`) returns {19=3*6+1}
• euclidean_division(`19/3`) returns {19=3*6+1}