What is long division?

Long division is a method for dividing a large number (the dividend) by another number (the divisor) digit by digit. At each step you ask how many times the divisor goes into the current partial dividend, write the result in the quotient, subtract the multiple from the partial dividend, and bring down the next digit. You repeat this until all digits of the dividend have been used, at which point any remaining value is the remainder.

What is the remainder in division?

The remainder is the amount left over after you have divided as evenly as possible. If you divide 17 by 5, the quotient is 3 (because 5 goes into 17 three times for a product of 15) and the remainder is 2 (because 17 minus 15 equals 2). A remainder of zero means the divisor divides the dividend exactly.

How do I check a long division answer?

Multiply the quotient by the divisor, then add the remainder. The result should equal the original dividend. For example, if 1547 divided by 7 gives a quotient of 221 and a remainder of 0, then 221 times 7 equals 1547. If the check does not match, there is an error somewhere in the working.

Long Division Calculator

This calculator performs long division on any two whole numbers and shows the complete step-by-step working so you can follow exactly how the answer is reached. Long division is the standard algorithm for dividing a large number by another number digit by digit. Each step involves asking how many times the divisor fits into the current portion of the dividend, writing that digit in the quotient, multiplying it back, subtracting the product, and bringing down the next digit of the dividend to continue. Learning to work through these steps helps build a solid understanding of how division relates to multiplication and remainders. To use the calculator, enter the dividend (the number being divided) and the divisor (the number you are dividing by). You receive the quotient, the remainder, and a numbered list of the working at every digit position. The steps show the current partial dividend, how many times the divisor fits, the product subtracted, and the remainder carried to the next step. Both the dividend and divisor must be positive whole numbers; the calculator handles cases where the divisor is larger than the dividend by returning a quotient of zero. This tool is aimed at primary and secondary school students learning division, parents helping with homework, and teachers demonstrating the algorithm. For division involving decimals or fractions, see the related tools below.

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Dividend (number to divide)

Divisor (divide by)

221

quotient

Remainder0

As decimal221.00

Check221 x 7 + 0 = 1547

Step-by-step working appears here.

How it works

The algorithm processes the dividend one digit at a time from left to right. At each position it appends the next digit to the current partial remainder to form the current partial dividend. It then calculates the largest whole-number multiple of the divisor that fits into the partial dividend (the quotient digit), records that digit in the running quotient, multiplies to get the product, and subtracts to find the new partial remainder. This continues until all digits of the dividend have been processed. The final partial remainder is the overall remainder. The check confirms the result: quotient times divisor plus remainder should equal the original dividend.

Worked example

Divide 1547 by 7. Start with 1: 7 does not go into 1, so the partial dividend becomes 15. 7 goes into 15 twice (product 14), remainder 1. Bring down 4 to get 14. 7 goes into 14 twice (product 14), remainder 0. Bring down 7 to get 7. 7 goes into 7 once (product 7), remainder 0. Quotient = 221, remainder = 0. Check: 221 × 7 = 1547.

Related calculators

Simplify Fractions: reduce a fraction to lowest terms after performing division.
Mixed Numbers Calculator: add, subtract, multiply or divide mixed numbers.
Percent to Fraction: convert a percentage to its simplest fraction form.
Percentage Calculator: work out percentage change, part of a whole, and more.

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