Long Division Calculator (Step by Step)

The long division calculator repeats four steps: divide, multiply, subtract, bring down. For 4,375 ÷ 12: 43 ÷ 12 = 3 (43 − 36 = 7), bring down 7 to make 77, 77 ÷ 12 = 6 (77 − 72 = 5), bring down 5 to make 55, 55 ÷ 12 = 4 (55 − 48 = 7). The answer is 364 R 7, or 364.58 with the 3 repeating.

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How to use the long division calculator

1. Type the dividend (the number being divided) and the divisor (the number you divide by). Whole numbers, decimals and negative numbers all work.
2. Choose how to show the answer: Remainder gives the quotient and remainder, such as 364 R 7. Decimal keeps dividing after the decimal point and marks repeating digits with a bar.
3. Follow the layout. Each dashed arrow shows a digit being brought down, each underline is a subtraction, and the red number at the bottom is the remainder.
4. Open Show steps for the working in words, and use the check box to confirm the answer by multiplication.

The parts of a division problem

The four parts are linked by one equation: divisor × quotient + remainder = dividend. Here 12 × 364 + 7 = 4,368 + 7 = 4,375, which is how you check any long division answer.

How to do long division step by step

Write the divisor outside the division bracket and the dividend inside it. Then repeat this cycle until every digit has been brought down:

1. Divide. Take the first digit (or the first few digits) of the dividend that is at least as big as the divisor, and find how many times the divisor fits. Write that digit in the quotient, above the last digit you used.
2. Multiply. Multiply the quotient digit by the divisor and write the product underneath.
3. Subtract. Subtract to find what is left. The difference must be smaller than the divisor; if it is not, the quotient digit was too small.
4. Bring down. Bring down the next digit of the dividend and write it next to the difference. Then divide again.

Worked example: 4,375 ÷ 12

The quotient is 364 and the remainder is 7, so 4,375 ÷ 12 = 364 R 7. As a mixed number this is 364 7/12.

Worked example with a zero in the quotient: 1,005 ÷ 5

5 goes into 10 twice (10 − 10 = 0). Bring down the 0: 5 does not go into 0, so write 0 in the quotient. Bring down the 5: 5 ÷ 5 = 1 with nothing left. The answer is 201. Skipping that 0 in the quotient is one of the most common long division mistakes, and it would give 21 instead.

Long division with remainders and with decimals

When the digits run out and something is left, you can stop and write a remainder, or keep going to get a decimal. To keep going, put a decimal point in the quotient directly above the point in the dividend, write a 0 after the dividend, and bring it down. Repeat as long as you need.

For 4,375 ÷ 12, the remainder 7 becomes 70: 70 ÷ 12 = 5 (70 − 60 = 10), then 100 ÷ 12 = 8 (100 − 96 = 4), then 40 ÷ 12 = 3 (40 − 36 = 4). The remainder 4 has come back, so the 3 repeats forever: 364.58333…, written with a bar over the 3.

Repeating and terminating decimals

A decimal ends (terminates) when a remainder of 0 appears. It repeats when a remainder you have seen before comes back, because from then on the same digits must follow. The repeating part can be short, as in 1 ÷ 3 = 0.333…, or long: 22 ÷ 7 = 3.142857142857…, where the six digits 142857 repeat. A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5.

Dividing by a decimal: move the point

Long division needs a whole-number divisor. If the divisor is a decimal, move its decimal point to the right until it is a whole number, and move the point in the dividend the same number of places. For 12.6 ÷ 0.3, move both points one place: 126 ÷ 3 = 42. Multiplying both numbers by the same power of 10 does not change the quotient.

A remainder in a decimal problem is in the scaled units, so divide it back. For 7.3 ÷ 0.5, the division 73 ÷ 5 = 14 R 3 means 7.3 ÷ 0.5 = 14 R 0.3, and the check is 0.5 × 14 + 0.3 = 7.3. As a decimal the answer is 14.6.

Dividing negative numbers

Divide the numbers without their signs, then apply the sign rules: if exactly one number is negative, the quotient is negative; if both are negative, it is positive. So −17 ÷ 5 = −3.4. With a remainder, most calculators and programming languages write −17 ÷ 5 = −3 R −2, because 5 × (−3) + (−2) = −17. Number theory prefers a remainder that is never negative, which gives −4 R 3, since 5 × (−4) + 3 = −17. The calculator shows both.

Common long division mistakes

• Leaving out a zero in the quotient. Every time you bring down a digit and the divisor does not fit, write 0 in the quotient before bringing down the next digit.
• A difference bigger than the divisor. If 77 − 60 = 17 with a divisor of 12, the quotient digit 5 was too small; use 6.
• Misplacing the digits. Write each quotient digit directly above the last dividend digit you used, or the place values shift.
• Forgetting to move both decimal points. When you shift the point in the divisor, shift it in the dividend too.

Polynomials are divided with the same divide, multiply, subtract, bring down routine. The polynomial division calculator shows that version step by step.

Using the long division calculator for homework

Do the problem on paper first, then type it in and compare the layout line by line. If your answer differs, look for the first row where your numbers and the calculator’s numbers disagree; that is where the mistake is. Before dividing, estimate: 4,375 ÷ 12 is a little more than 4,000 ÷ 12 ≈ 333, so an answer near 364 is reasonable, while 36 or 3,640 is not. On a test, always finish with the multiplication check.

Long Division practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is long division?

Long division is a written method for dividing large numbers by breaking the problem into small steps: divide, multiply, subtract and bring down, one digit at a time. It gives a quotient and a remainder, or a decimal if you keep going.

How do you do long division with remainders?

Work through the digits as usual. When there are no digits left to bring down, the last difference is the remainder, and it must be smaller than the divisor. For 7,425 ÷ 6 the answer is 1,237 R 3, because 6 × 1,237 + 3 = 7,425.

How do you do long division with decimals?

If the divisor is a decimal, move its point to make it whole and move the dividend's point the same number of places. Then divide normally, keeping the decimal point in the quotient directly above the point in the dividend, and add zeros to the dividend if you need more decimal places.

How do you check a long division answer?

Multiply the quotient by the divisor and add the remainder. You should get the dividend back. For 4,375 ÷ 12 = 364 R 7, 12 × 364 + 7 = 4,375.

Can you do long division on a calculator?

A basic calculator gives only the decimal, such as 364.5833. To get the remainder, multiply the whole-number part by the divisor and subtract from the dividend: 4,375 − 12 × 364 = 7. This long division calculator shows the full written layout as well.

Is long division hard?

It has many steps, but each step is simple multiplication and subtraction. Knowing your times tables, writing digits in neat columns and checking each difference is smaller than the divisor makes it much easier.

Related calculators

• Long multiplication calculator: the column method with carries, and the check for division
• Polynomial division calculator: long division of polynomials
• Fraction, decimal and percent calculator: convert quotients between forms
• Rounding calculator: round a long decimal answer