Long division is a step-by-step method for dividing large numbers that are hard to divide in your head. You work through the dividend one digit at a time, repeating the same four steps — divide, multiply, subtract, bring down — until every digit is used up. On this page you'll find the four steps explained, a full worked example, how to handle remainders and larger numbers, and an interactive trainer so you can practice right away.
What is long division?
Long division is a way to divide one number (the dividend) by another (the divisor) when the numbers are too big to divide mentally. The answer you build up on top is called the quotient, and anything left over at the end is the remainder.
The key idea is that you don't divide the whole number at once. Instead you look at the dividend one digit at a time, from left to right, and repeat a short cycle of steps for each digit. Because you always follow the same routine, even a large division problem becomes a series of small, easy divisions.
The steps of long division: divide, multiply, subtract, bring down
Long division repeats the same four steps for each digit of the dividend. Many students remember them by the phrase D → M → S → B: Divide, Multiply, Subtract, Bring down. After you bring down a digit, you go back to the top and repeat — that's why it's called a cycle.
Long division example: 528 ÷ 4
Let's divide 528 ÷ 4 step by step. We write 4 outside the bracket (the divisor) and 528 inside (the dividend), then work left to right.
- Divide: 5 ÷ 4 = 1. Write 1 above the 5. Multiply: 1 × 4 = 4. Subtract: 5 − 4 = 1. Bring down the 2 → you now have 12.
- Divide: 12 ÷ 4 = 3. Write 3 in the quotient. Multiply: 3 × 4 = 12. Subtract: 12 − 12 = 0. Bring down the 8 → you now have 8.
- Divide: 8 ÷ 4 = 2. Write 2 in the quotient. Multiply: 2 × 4 = 8. Subtract: 8 − 8 = 0. Nothing left to bring down.
The quotient on top reads 132, and the final subtraction gives 0, so there is no remainder: 528 ÷ 4 = 132.
Long division with remainders
Not every division comes out evenly. When the last subtraction leaves a number that is not zero, that leftover is the remainder. A remainder is always smaller than the divisor — if it isn't, the divisor still goes in at least one more time, so you haven't finished dividing.
Here is 617 ÷ 5. Working left to right: 6 ÷ 5 = 1 remainder 1; bring down the 1 to make 11, and 11 ÷ 5 = 2 remainder 1; bring down the 7 to make 17, and 17 ÷ 5 = 3 remainder 2. There are no more digits to bring down, so the leftover 2 is the remainder: 617 ÷ 5 = 123 remainder 2. You can write the answer as 123 R2.
Dividing large numbers
The same four steps work no matter how many digits the dividend has — a 4-digit or 5-digit number is just a few more rounds of divide, multiply, subtract, bring down. A couple of tips make big divisions easier:
- Keep your columns lined up. Write each quotient digit directly above the digit you are working on, and keep the numbers underneath in neat columns. Most mistakes in long division come from digits drifting sideways.
- Don't skip the zero. If the divisor doesn't fit into the current number (for example, 1 ÷ 6), you still write a 0 in the quotient and then bring down the next digit. Skipping it makes the answer ten times too small.
- Estimate first. Before dividing large numbers, a quick estimate (about how big should the answer be?) helps you catch errors — if you expect a 3-digit answer and get a 2-digit one, something went wrong.
When you finish, you can always check your work: multiply the quotient by the divisor and add the remainder. If you get the original dividend back, your answer is correct.
Long division examples
Example 1: 528 ÷ 4 = 132 (no remainder)
Divide the hundreds: 5 ÷ 4 = 1. Write 1 above the 5. Multiply 1 × 4 = 4, subtract 5 − 4 = 1, and bring down the 2 to make 12.
Divide the tens: 12 ÷ 4 = 3. Write 3. Multiply 3 × 4 = 12, subtract 12 − 12 = 0, and bring down the 8.
Divide the ones: 8 ÷ 4 = 2. Write 2. Multiply 2 × 4 = 8, subtract 8 − 8 = 0. Nothing is left.
Answer: 528 ÷ 4 = 132. Check: 132 × 4 = 528. ✓
Example 2: 617 ÷ 5 = 123 R2 (with remainder)
Divide: 6 ÷ 5 = 1 (write 1), 1 × 5 = 5, 6 − 5 = 1, bring down the 1 → 11.
Divide: 11 ÷ 5 = 2 (write 2), 2 × 5 = 10, 11 − 10 = 1, bring down the 7 → 17.
Divide: 17 ÷ 5 = 3 (write 3), 3 × 5 = 15, 17 − 15 = 2. No more digits to bring down.
Answer: 617 ÷ 5 = 123 remainder 2 (written 123 R2). Check: 123 × 5 + 2 = 615 + 2 = 617. ✓
Example 3: 618 ÷ 6 = 103 (a zero in the quotient)
Divide: 6 ÷ 6 = 1 (write 1), 6 − 6 = 0, bring down the 1 → 1.
Divide: 1 ÷ 6 = 0. The 6 does not fit into 1, so you write a 0 in the quotient. Bring down the 8 → 18.
Divide: 18 ÷ 6 = 3 (write 3), 18 − 18 = 0.
Answer: 618 ÷ 6 = 103. That middle zero is easy to forget — without it you'd wrongly get 13. Check: 103 × 6 = 618. ✓
Common long division mistakes
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Forgetting to bring down the next digit before dividing again.
After every subtraction, bring down the next digit of the dividend and place it next to the result. Only stop when there are no digits left to bring down. Skipping this step leaves out part of the answer.
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Misaligning the digits so the columns drift sideways.
Write each quotient digit directly above the digit you are dividing, and keep the numbers underneath in straight columns. Using grid paper (one digit per box) keeps ones under ones and tens under tens.
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Leaving a remainder that is equal to or larger than the divisor.
A remainder must be smaller than the divisor. If your leftover is as big as the divisor (or bigger), the divisor still goes in at least one more time — you subtracted too little, so the quotient digit should be larger.
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Forgetting to write a zero in the quotient when a step doesn't divide.
If the divisor doesn't fit into the current number (for example, 1 ÷ 6), still write a 0 in the quotient before bringing down the next digit. Leaving it out drops a place value and makes the answer ten times too small (13 instead of 103).
Long division: questions and answers
What is long division?
Long division is a written method for dividing numbers that are too large to divide in your head. You divide the dividend one digit at a time from left to right, repeating four steps — divide, multiply, subtract, bring down — to build up the answer (the quotient), with any leftover shown as a remainder.
What are the steps of long division?
There are four repeating steps, often remembered as D-M-S-B: Divide (how many times does the divisor go in?), Multiply (the quotient digit by the divisor), Subtract (the product from the number above), and Bring down (the next digit). Then you repeat the cycle until every digit has been used.
How do you do long division with remainders?
Do the division exactly the same way. When you reach the last digit and the final subtraction does not come out to zero, that leftover number is the remainder. It is always smaller than the divisor. For example, 617 ÷ 5 = 123 remainder 2, which you can write as 123 R2.
How do you divide large numbers using long division?
The method doesn't change for big numbers — you just repeat the divide-multiply-subtract-bring-down cycle for each extra digit. Keep your columns lined up, and remember to write a 0 in the quotient whenever the divisor doesn't fit into the current digit before you bring down the next one.
How do you check a long division answer?
Multiply the quotient by the divisor, then add the remainder. If the result equals the original dividend, your answer is correct. For 617 ÷ 5 = 123 R2, the check is 123 × 5 + 2 = 617. ✓
What does the remainder mean?
The remainder is the amount left over that could not be shared evenly. If you divide 47 cookies among 5 friends, each gets 9 and there are 2 cookies left over — that 2 is the remainder. It is always less than the number you are dividing by.
