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Calculator Answers

Long Division Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A long division calculator is an educational tool that divides one integer by another, displaying the complete sequence of arithmetic steps required to reach the solution. It accepts a dividend and a divisor, producing the quotient and the remainder, or alternatively, a decimal representation and mixed fraction form. The calculator demonstrates the traditional long division algorithm by showing the repeated steps of division, multiplication, subtraction, and bringing down digits. Students and educators use it to learn, practice, and verify multi-digit division steps and remainders.

Enter the dividend and divisor and the calculator returns the quotient, remainder, decimal result, and a mixed-number form when the division does not come out even.

See also: Polynomial Long Division Calculator, Synthetic Division Calculator, and Scientific Notation Calculator.

Quick Answer

Perform long division with remainders or decimals. Enter the dividend and divisor to see the quotient and step-by-step arithmetic work.

The number being divided. · e.g. 754

Cannot be 0. · e.g. 3

Long division works best with whole numbers. Decimal inputs still return a decimal result.

Long division

Quotient with remainder

251 R 1

754 ÷ 3

Dividend754
Divisor3
Quotient251
Remainder1
Mixed number251 1/3
Decimal251.3333333333

Dividend = divisor × quotient + remainder. Here 754 = 3 × 251 + 1.

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Examples

754 ÷ 3

= 251 R 1 · mixed 251 1/3 · decimal 251.333…

1000 ÷ 25

= 40 · no remainder

97 ÷ 12

= 8 R 1 · mixed 8 1/12 · decimal 8.0833…

How it works

Long division finds the largest whole-number multiple of the divisor that fits in the dividend. The quotient is that whole number; the remainder is what is left over. Long division is an integer procedure, so decimal inputs only return a decimal answer.

Definition · dividend = divisor × quotient + remainder

Mixed form · quotient + remainder / divisor

Whole-number inputs give a clean quotient and remainder.

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More tools from Education

Polynomial Long Division CalculatorDivide one polynomial by another using polynomial long division. Enter coefficients for the dividend and divisor; the calculator returns the quotient, the remainder, and a step-by-step trace.Synthetic Division CalculatorDivide a polynomial by x - c using synthetic division. Enter the polynomial coefficients and the divisor value c; the calculator returns the quotient coefficients, the remainder, and the full synthetic table step by step.Scientific Notation CalculatorConvert standard numbers to scientific notation (a × 10^b) and back. Returns the coefficient, exponent, and a short explanation of the decimal-point shift.Remainder CalculatorFind the quotient and a non-negative remainder from integer division. Returns the division statement and modulo notation.

Frequently asked questions

Long division is a written procedure for dividing one whole number (the dividend) by another (the divisor). It produces an integer quotient and a non-negative remainder less than the divisor. The relationship is dividend = divisor × quotient + remainder.

The remainder is what is left over after the divisor goes into the dividend as many whole times as possible. For example, 754 ÷ 3 gives quotient 251 with remainder 1, because 3 × 251 = 753 and the dividend is 754. Continuing the division past the decimal point turns the remainder into the decimal portion of the answer.

Yes, but long division as a written method is built for whole numbers. With decimal inputs the calculator returns only the decimal answer and does not show a quotient and remainder. Convert decimals to whole numbers first if you need a clean remainder.

Division by 0 is undefined. The calculator flags the input and returns no answer. Make sure the divisor is a nonzero number.

The calculator follows the standard rule dividend = divisor × quotient + remainder, with the quotient sign chosen so the remainder is non-negative in absolute value. For an everyday whole-number division like -754 ÷ 3, this returns quotient -251 and remainder -1 in signed form, equivalent to -(251 remainder 1).

When the remainder is not 0, the answer can be written as a whole-number quotient plus a fraction. For 754 ÷ 3, the quotient is 251 and the remainder is 1 over divisor 3, giving the mixed number 251 1/3. The decimal form is 251.333…