Long Division Calculator

This long division calculator helps you divide whole numbers and decimals while showing the work step by step.

Long Division Calculator

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Keep decimal places in the steps.

How to Calculate a Long Division Problem

Long division is a step-by-step way to divide a large number. The number being divided is the dividend, and the number you divide by is the divisor.

Example: in 200 ÷ 13, 200 is the dividend and 13 is the divisor.

Long Division Calculator: Components of Division

In written long division, place the dividend inside the division bracket and the divisor on the outside. Then follow a repeating pattern: divide, multiply, subtract, and bring down the next digit.


13		2	0	0

Step 1: Find the first number the divisor can fit into

Start from the left side of the dividend. In 200 ÷ 13, the first digit is 2. Since 13 cannot fit into 2, look at the first two digits: 20.

	0

13	2	0	0

Some teachers write a zero above the first digit. Others begin the quotient above the digit where the actual division starts. Both layouts are common.

Step 2: Divide and write the first quotient digit

Ask: how many times does 13 fit into 20? It fits 1 time.

	0	1

13	2	0	0
	1	3

Write 1 in the quotient, then multiply: 13 × 1 = 13.

Step 3: Subtract and bring down the next digit

Subtract 13 from 20: 20 - 13 = 7.

		0	1

13		2	0	0
	-	1	3	↓

			7	0

Then bring down the next digit, which is 0. Now the working number becomes 70.

Step 4: Repeat divide, multiply, and subtract

Now ask: how many times does 13 fit into 70? It fits 5 times because 13 × 5 = 65.

Subtract: 70 - 65 = 5.

		0	1	5

13		2	0	0
	-	1	3	↓

			7	0
		-	6	5

				5

So the whole-number result is: 200 ÷ 13 = 15 remainder 5.

Step 5: Continue into decimals if needed

If you want a decimal answer, add a decimal point after the quotient and bring down a zero. The remainder 5 becomes 50.

		0	1	5	.	3

13		2	0	0
	-	1	3	↓

			7	0
		-	6	5		↓

				5		0
			-	3		9

				1		1

Then continue the same pattern. For this example: 200 ÷ 13 = 15.384615384615....

		0	1	5	.	3	8

13		2	0	0
	-	1	3	↓

			7	0
		-	6	5		↓

				5		0
			-	3		9	↓

				1		1	0
			-	1		0	4

							6

Teacher Tip: If a student is confused, ask them to say each step aloud: “Divide, multiply, subtract, bring down.” This simple rhythm helps prevent skipped steps.

Why Students Often Get Long Division Wrong

Long division is not hard because of one single operation. It becomes tricky because students must keep track of several small steps in the correct order. Here are the most common mistakes and how to avoid them.

1. Forgetting to bring down a zero

When continuing into decimals, students often forget to add or bring down a zero after the decimal point.

Fix: If there is a remainder and you want decimals, add a zero and keep dividing.

2. Leaving a remainder larger than the divisor

A remainder must always be smaller than the divisor. If the remainder is equal to or larger than the divisor, the quotient digit was too small.

Fix: Check that the remainder is less than the divisor before moving on.

3. Placing the decimal point in the wrong spot

When decimals are involved, students may put the decimal point above the wrong place.

Fix: The decimal point in the quotient should line up with the decimal point in the dividend after any necessary adjustment.

4. Multiplying correctly but subtracting incorrectly

A student may choose the right quotient digit but make a small subtraction error.

Fix: After each subtraction, quickly add the answer back to the product to check it.

5. Writing the quotient digit above the wrong digit

In long division, place value matters. A digit written one space too far left or right changes the entire answer.

Fix: Write each quotient digit directly above the digit currently being used.

6. Stopping too early

Students may stop when there is a remainder even though the question asks for a decimal answer.

Fix: Read the instruction carefully: remainder form, fraction form, or decimal form.

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What This Long Division Calculator Shows

Quotient: the main answer to the division problem.
Remainder: the amount left over when the divisor cannot fit evenly into the dividend.
Decimal result: the quotient written as a decimal, useful when you do not want remainder form.
Step-by-step work: each divide, multiply, subtract, and bring-down step.
Decimal-place control: choose how many decimal places to show in the long division steps.
Printable worksheet: generate a practice page with blank workspace and a separate answer page.

FAQ

What is the dividend?

The dividend is the number being shared or split. For example, if you have 200 apples and want to divide them among groups, then 200 is the dividend.

What is the divisor?

The divisor tells you the size of each group or how many groups you are dividing by. In 200 ÷ 13, the divisor is 13. You are checking how many groups of 13 can fit into 200.

What does the remainder mean?

Imagine 13 children are sharing 200 apples equally. Each child can get 15 apples, which uses 195 apples. There are 5 apples left. Those 5 apples are the remainder.

So, 200 ÷ 13 = 15 remainder 5.

When should I use a remainder instead of a decimal?

Use a remainder when the leftover amount is meaningful as a whole item. For example, if you are packing students into buses, a remainder means you may need another bus. A decimal answer may not make sense in that situation.

When should I continue into decimals?

Use decimals when the amount can be split into smaller parts. For example, money, measurements, distance, and weight often use decimal answers.

Why do some long division answers repeat forever?

A decimal repeats when the same remainder appears again during the division process. For example, 200 ÷ 13 becomes 15.384615384615... because the remainder pattern repeats.

How can I check a long division answer?

Use this rule:

Divisor × Quotient + Remainder = Dividend

For example: 13 × 15 + 5 = 200. Since the result is 200, the answer is correct.

Why is my remainder bigger than the divisor?

If your remainder is bigger than or equal to the divisor, you probably chose a quotient digit that was too small. The remainder should always be smaller than the divisor.

References

For additional explanations and practice materials related to long division, you may find these resources helpful:

These links are provided as math-learning references. They do not imply endorsement of this calculator.

Long Division Calculator