Long Division Calculator: Divide Step By Step With Remainders

Long division is the method for dividing large numbers by hand, one digit at a time. It looks long on paper, but it is just one short cycle repeated. This guide shows that cycle with whole numbers, remainders, two-digit divisors, decimals and polynomials. Every example was checked in Python.

Note: Calc Solver (calc-solver.co) is an independent guide site and is not affiliated with any calculator mentioned here.

The Parts Of A Division Problem

Every division problem has four parts. Knowing the names makes the steps easier to follow.

The same problem can be written three ways: 437 ÷ 6, 437/6, or with the long division bracket, where 437 sits inside the bracket and 6 sits outside to the left. In the bracket layout, the quotient is written on top.

The parts always fit this rule: dividend = quotient × divisor + remainder. For our example, 72 × 6 + 5 = 437. This rule is the fastest way to check any answer.

How To Use The Long Division Calculator

The long division calculator above shows the work the way schools teach it. It takes three steps:

1. Pick a tab. Use Whole Numbers for most homework, Decimals when either number has a decimal point, or Polynomials for algebra.
2. Enter the dividend and divisor. The dividend goes first, the number you are dividing.
3. Step through the work. Press "Next step" to build the answer one digit at a time, or "Show all" to see the full layout.

The result appears in three forms: with a remainder, as a mixed number and as a decimal. Use whichever form your teacher asks for.

The Four Steps Of Long Division

Long division repeats four steps until there are no digits left to bring down: Divide, Multiply, Subtract, Bring down. Many students remember the order with the phrase "Does McDonald's Sell Burgers?"

1. Divide: see how many times the divisor fits into the current number.
2. Multiply: multiply that digit by the divisor.
3. Subtract: take the product away from the current number.
4. Bring down: move the next digit of the dividend down next to the result.

After each subtraction, the result must be smaller than the divisor. If it is not, the digit you chose in the Divide step was too small.

Long Division With A One-Digit Divisor

A one-digit divisor is the best place to learn the cycle. Here is 852 ÷ 4.

1. Divide: 4 goes into 8 two times. Write 2 on top.
2. Multiply and subtract: 2 × 4 = 8, and 8 − 8 = 0.
3. Bring down the 5. Now 4 goes into 5 one time. Write 1 on top.
4. Multiply and subtract: 1 × 4 = 4, and 5 − 4 = 1.
5. Bring down the 2 to make 12. 4 goes into 12 three times. Write 3 on top.
6. Multiply and subtract: 3 × 4 = 12, and 12 − 12 = 0.

There are no digits left and the remainder is 0, so 852 ÷ 4 = 213.

Long Division With A Remainder

When the last subtraction does not reach zero, what is left is the remainder. Here is 437 ÷ 6, laid out the way it looks on paper:

72 R5

____

6 ) 437

42

—

17

12

—

5

1. 6 does not go into 4, so start with 43. 6 goes into 43 seven times (42). 43 − 42 = 1.
2. Bring down the 7 to make 17. 6 goes into 17 two times (12). 17 − 12 = 5.
3. No digits are left, so 5 is the remainder.

437 ÷ 6 = 72 R5. Check: 72 × 6 = 432, and 432 + 5 = 437.

When A Zero Goes In The Quotient

If the divisor does not fit into a number after you bring down a digit, you must write a 0 in the quotient before bringing down the next digit. Skipping this zero is one of the most common long division mistakes.

For 612 ÷ 6: 6 goes into 6 once, leaving 0. Bring down the 1. Since 6 does not go into 1, write 0 on top. Bring down the 2 to make 12, and 6 goes into 12 twice. The answer is 102, not 12.

Long Division With A Two-Digit Divisor

With a two-digit divisor, the hard part is guessing each digit. Round the divisor to the nearest ten to estimate, then adjust if needed.

Solve 7,644 ÷ 28. Round 28 up to 30 to make estimates easy.

So 7,644 ÷ 28 = 273.

Notice that the estimates were sometimes one too low. Rounding the divisor up makes the guess low, so if your remainder after subtracting is still bigger than the divisor, raise the digit by one. If the product is bigger than the current number, lower it by one.

A second example with a remainder: 2,345 ÷ 15 = 156 R5. Check: 156 × 15 = 2,340, and 2,340 + 5 = 2,345.

A Trick For Big Divisors: Make A Multiples List

A simple trick for bigger divisors is to write the divisor's multiples before you start. Then each Divide step becomes a lookup instead of a guess.

For 28, the list is 28, 56, 84, 112, 140, 168, 196, 224 and 252. When you reach 204 in the problem above, you can see right away that 196 (7 × 28) is the largest multiple that fits. This takes a minute up front but prevents most estimate-and-erase cycles, especially on tests.

Long Division With A Three-Digit Divisor

The steps do not change with a three-digit divisor. You just look at more digits of the dividend at the start, and the multiples list matters even more.

Solve 45,678 ÷ 123. The multiples of 123 are 123, 246, 369, 492, 615, 738, 861, 984 and 1,107.

1. 123 does not fit into 4 or 45, so start with 456. The largest multiple that fits is 369 (3 × 123). Write 3. 456 − 369 = 87.
2. Bring down 7 to make 877. The largest multiple that fits is 861 (7 × 123). Write 7. 877 − 861 = 16.
3. Bring down 8 to make 168. 123 fits once. Write 1. 168 − 123 = 45.

So 45,678 ÷ 123 = 371 R45. Check: 371 × 123 = 45,633, and 45,633 + 45 = 45,678.

Dividing Negative Numbers

Long division works the same with negative numbers. Divide the numbers as if they were positive, then apply the sign rule.

• Same signs give a positive answer: −84 ÷ −7 = 12.
• Different signs give a negative answer: −84 ÷ 7 = −12 and 84 ÷ −7 = −12.

With a remainder, school math usually keeps the remainder positive and puts the sign on the quotient. Some calculators and programming languages handle negative remainders differently, so check which rule your class uses.

Three Ways To Write The Answer

A remainder can be written as a whole number, a fraction or a decimal. They all mean the same amount.

To get the decimal, write a decimal point after the dividend, add zeros and keep going. The next section shows how. If you need to simplify the fraction part, the fraction calculator reduces it for you.

Long Division With Decimal Answers

To continue past the remainder, put a decimal point in the quotient directly above the one in the dividend, then add zeros to the dividend and keep dividing.

Solve 7 ÷ 8. Since 8 does not go into 7, write 0 and a decimal point, then think of 7 as 7.000.

1. 8 goes into 70 eight times (64). Remainder 6.
2. Bring down a 0 to make 60. 8 goes in seven times (56). Remainder 4.
3. Bring down a 0 to make 40. 8 goes in five times (40). Remainder 0.

So 7 ÷ 8 = 0.875. It stops because the remainder reached zero. This is called a terminating decimal.

Repeating Decimals In Long Division

Some divisions never reach a remainder of zero. Instead, a remainder repeats, and the digits start repeating with it.

Solve 1 ÷ 7. The remainders go 3, 2, 6, 4, 5, 1, and then 1 again. Once a remainder repeats, the digits will too. So 1 ÷ 7 = 0.142857142857…, written with a bar over 142857.

You can predict which kind you will get. Simplify the fraction first. If the denominator's only prime factors are 2 and 5, the decimal terminates. If it has any other prime factor, like 3 or 7, the decimal repeats. That is why 7/8 terminates (8 = 2³) but 5/12 repeats as 0.41666…, because 12 = 2² × 3. The factor calculator shows a number's prime factors.

Dividing Decimals By Decimals

When the divisor has a decimal point, move it to the right until the divisor is a whole number. Then move the decimal point in the dividend the same number of places.

Solve 9.45 ÷ 0.35:

1. Move the decimal two places in 0.35 to get 35.
2. Move it two places in 9.45 to get 945.
3. Divide: 945 ÷ 35 = 27.

This works because you multiplied both numbers by 100, and the answer of a division does not change when both numbers are scaled by the same amount. If the dividend runs out of digits, add zeros so you can keep moving the point.

Long Division Vs Short Division

Short division is a faster way to write the same steps when the divisor is a single digit. You do the multiply and subtract in your head and write only the small remainder next to the next digit.

Both methods give the same answer. Teachers usually want long division until the steps are second nature.

What The Remainder Means In Word Problems

In a word problem, the remainder decides the final answer, and the right choice depends on the question. You might round up, drop it, or split it further.

Always reread the question after you divide. A bus answer of 5.625 makes no sense, and 5 buses would leave students behind.

Polynomial Long Division

Polynomial long division uses the same four steps with algebra terms instead of digits. Divide the leading terms, multiply, subtract and bring down the next term.

Solve (x³ − 2x² − 4) ÷ (x − 3). First, fill in the missing x term with 0x, so the dividend is x³ − 2x² + 0x − 4.

1. Divide: x³ ÷ x = x². Multiply: x²(x − 3) = x³ − 3x². Subtract: x². Bring down 0x.
2. Divide: x² ÷ x = x. Multiply: x(x − 3) = x² − 3x. Subtract: 3x. Bring down −4.
3. Divide: 3x ÷ x = 3. Multiply: 3(x − 3) = 3x − 9. Subtract: 5.

So the quotient is x² + x + 3 with a remainder of 5. You can also write it as x² + x + 3 + 5/(x − 3).

When the divisor has the form x − c, synthetic division is a shortcut. Use c = 3 and the coefficients 1, −2, 0, −4. Bring down the 1, multiply by 3 and add each time: 1, 1, 3, then 5. The last number is the remainder, and the rest are the quotient's coefficients.

If the remainder is 0, the divisor is a factor. For example, (2x² + 5x − 3) ÷ (x + 3) = 2x − 1 with no remainder, so 2x² + 5x − 3 = (x + 3)(2x − 1).

How To Check A Long Division Answer

The check is always the same: multiply the quotient by the divisor, then add the remainder. If you get the dividend back, the answer is right.

• 7,644 ÷ 28 = 273. Check: 273 × 28 = 7,644. Correct.
• 1,000 ÷ 7 = 142 R6. Check: 142 × 7 = 994, and 994 + 6 = 1,000. Correct.

A quick estimate also catches big slips. For 7,644 ÷ 28, think 7,500 ÷ 25 = 300. An answer near 300 makes sense, and an answer like 27 or 2,730 means a digit went missing or got added. The scientific calculator is handy for checking the multiplication.

Common Long Division Mistakes

Most long division errors come from skipping a zero or misplacing a digit.

Summary

• Long division repeats four steps: divide, multiply, subtract, bring down.
• Write a 0 in the quotient whenever the divisor does not fit.
• Round a two-digit divisor to estimate each digit, then adjust by one if needed.
• Write remainders as R, a fraction or a decimal. Add zeros after the decimal point to keep dividing.
• Decimals repeat when the simplified denominator has a prime factor other than 2 or 5.
• Check every answer with quotient × divisor + remainder = dividend.

Next step: enter your problem in the long division calculator at the top of this page and step through it digit by digit. For more math tools, visit the Calc Solver homepage.

Frequently Asked Questions