Long Division Calculator

How to use this tool

Type the number you are dividing, the dividend, and the number you are dividing by, the divisor. The long division appears drawn the way it is written in class, with the answer on top, and every step is listed below it in words. Choose decimal places to carry the division on past the decimal point instead of stopping at a remainder.

The input people most often swap is the order: 1234 ÷ 7 means 1234 is the dividend. Decimals work in either box; the tool moves the decimal point first and tells you what it did.

How long division works

Long division breaks a big division into a chain of small ones, one digit at a time. Each step asks how many times the divisor fits into the part of the number you are looking at, writes that digit in the answer, and carries whatever is left over into the next digit. That leftover is always smaller than the divisor, which is why each step only ever needs a single digit.

The same leftover explains repeating decimals. Carrying on past the decimal point, each step can only leave one of a limited set of remainders, so sooner or later one comes back and the digits from there repeat. The calculator watches for that and marks the repeating part in brackets.

Unit fractions as long division

A worked example you can check on paper

Take 1234 ÷ 7, the calculator’s starting example. 7 does not go into 1, so start with 12: 7 goes in once, 1 x 7 = 7, and 12 – 7 = 5. Bring down the 3 to make 53: 7 goes in 7 times, 49, leaving 4. Bring down the 4 to make 44: 7 goes in 6 times, 42, leaving 2.

The answer is 176 remainder 2, and the check works: 7 x 176 = 1232, plus 2 is 1234. Carrying on with zeros after the point gives 176.285714, and the digits 285714 then repeat, the same six digits as 2/7.

Mistakes that catch people out

Dropping a zero in the answer. When the divisor does not go into the number brought down, write 0 in the quotient before bringing down the next digit. 1015 ÷ 5 is 203, not 23.

A remainder bigger than the divisor. If what is left after subtracting is as big as the divisor, the digit above was too small; go back and add one.

Moving the point in only one number. When dividing by a decimal, shift the point in both numbers by the same amount, or the answer is out by a power of ten.

Rounding a repeating decimal as if it ended. 2/3 is 0.666 repeating, which rounds to 0.67, not 0.66.

Popular calculations

Each opens the calculator with that division worked out, and the numbers can be changed once it is open.

Whole numbers with remainders

Repeating and terminating decimals

Dividing decimals

How this was checked

The engine uses whole number arithmetic that is exact at any length, and every result was checked by multiplying back: divisor x quotient + remainder = dividend. Repeating decimals were compared with known expansions, such as 1/7 = 0.(142857) and 7/12 = 0.58(3), and an 18 digit dividend was divided without any rounding.

Every address in the lists above was then opened and checked for a distinct title, the right answer, a layout and chart that render, and clean CSV, image and print output containing only that division, at desktop, tablet and phone widths.

Common questions

How do you do long division step by step?

Work from the left of the dividend. Divide the divisor into as many digits as you need, write that digit of the answer on top, multiply it by the divisor, subtract, then bring down the next digit and repeat. For 1234 ÷ 7: 7 into 12 goes 1, leaving 5; 53 gives 7, leaving 4; 44 gives 6, leaving 2. The answer is 176 remainder 2.

How do you write a remainder as a decimal?

Keep going past the decimal point: put a point after the dividend, add zeros and carry on dividing. For 1234 ÷ 7, the remainder 2 becomes 20, which gives 2 more digits, and so on: 176.285714 and the six digits keep repeating. Or divide the remainder by the divisor, 2 ÷ 7 = 0.2857.

How do you divide by a decimal?

Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. 12.5 ÷ 0.25 becomes 1250 ÷ 25 = 50. Multiplying both numbers by the same amount does not change the answer.

Why do some divisions never end?

Each step leaves a remainder smaller than the divisor, so there are only so many possible remainders. If one comes back, the digits from that point repeat for ever. A division ends only when the fraction in lowest terms has a denominator made of 2s and 5s, which is why 1/8 = 0.125 ends and 1/3 does not.

What do dividend, divisor, quotient and remainder mean?

In 1234 ÷ 7 = 176 R 2, 1234 is the dividend, 7 the divisor, 176 the quotient and 2 the remainder. They always fit the check: divisor x quotient + remainder = dividend, so 7 x 176 + 2 = 1234.

What happens when you divide by zero?

There is no answer. Division asks how many times the divisor fits into the dividend, and no number of zeros adds up to anything but zero, so the calculator shows no result for a divisor of 0.

Related Calculators and Reference

• Fraction Calculator: work with the answer as a fraction.
• Decimal to Fraction Converter: turn a decimal back into a fraction.
• Prime Factorisation Calculator: why some decimals end and others repeat.
• Percentage Calculator: division written as a percent.
• NCTM: Number and Operations Standards: where long division sits in school maths.