Long Division Calculator
Divide two whole numbers with long division, and see the quotient, the remainder, the decimal answer and every step.
Results
| Item | Value |
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Steps
| Step | Working |
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Quick Answer
Long division splits a number into equal groups one digit at a time: divide, multiply, subtract, then bring down the next digit. 4,567 ÷ 12 = 380 remainder 7, because 380 × 12 = 4,560 and 4,567 − 4,560 = 7. As a decimal, that is about 380.5833.
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Table of Contents
- Long Division Calculator
- Quick Answer
- Related Calculators
- How This Long Division Calculator Works
- How to Use the Long Division Calculator
- The Long Division Steps
- Key Terms
- Worked Example
- Real-Life Examples
- Long Division vs Short Division
- Division Terms at a Glance
- Tips for Long Division
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Long Division Calculator Works
Enter the dividend (the number being divided) and the divisor (the number you divide by). The calculator works through the dividend one digit at a time, just as you would on paper, and shows every step.
Quick explanation: dividend = divisor × quotient + remainder.
- Quotient: how many whole times the divisor fits.
- Remainder: what is left over, always smaller than the divisor.
- Decimal answer: the full result to the places you choose.
How to Use the Long Division Calculator
- Enter the dividend, the number you want to divide.
- Enter the divisor, the number you are dividing by.
- Choose how many decimal places you want for the decimal answer.
- Press Calculate.
- Read the quotient, remainder and decimal answer, then follow the steps table.
The Long Division Steps
- Divide: how many times does the divisor fit into the current number?
- Multiply: multiply that digit by the divisor.
- Subtract: take the product away from the current number.
- Bring down: bring down the next digit of the dividend and repeat.
A common memory aid is “Does McDonald’s Sell Burgers?” for Divide, Multiply, Subtract, Bring down.
Key Terms
- Dividend: the number being divided.
- Divisor: the number you divide by.
- Quotient: the whole-number result of the division.
- Remainder: the amount left over that cannot be divided evenly.
- Divisible: a number is divisible by another if the remainder is 0.
Worked Example
Divide 4,567 by 12.
- 45 ÷ 12 = 3, 3 × 12 = 36, 45 − 36 = 9
- Bring down 6 to make 96. 96 ÷ 12 = 8, 8 × 12 = 96, 96 − 96 = 0
- Bring down 7 to make 7. 7 ÷ 12 = 0, so the remainder is 7
- Answer: 380 R 7, or about 380.5833
Real-Life Examples
- Sharing equally: 1,250 stickers shared among 8 children is 156 each, with 2 left over.
- Packing boxes: 500 items in boxes of 24 fill 20 boxes, with 20 items left over, so you need 21 boxes.
- Splitting a bill: $347 split 6 ways is $57 each with $5 left, or about $57.83 each as a decimal.
- Homework checks: enter your problem to compare each step with your own working.
Long Division vs Short Division
- Long division: writes out every multiply and subtract step. Best for larger divisors.
- Short division: does the subtraction in your head and writes only the carries. Faster for single-digit divisors.
- Same answer: both methods give the same quotient and remainder.
Division Terms at a Glance
| Term | In 4,567 ÷ 12 = 380 R 7 |
|---|---|
| Dividend | 4,567 |
| Divisor | 12 |
| Quotient | 380 |
| Remainder | 7 |
Tips for Long Division
- Write a times table: list the divisor × 1 to 9 before you start.
- Keep columns lined up: it stops digits sliding into the wrong place.
- Write zeros: if the divisor does not fit, write 0 in the quotient.
- Check your answer: quotient × divisor + remainder should equal the dividend.
Common Mistakes to Avoid
- Forgetting a zero in the quotient. If the divisor does not fit, you still write 0.
- Leaving a remainder bigger than the divisor. That means the last digit of the quotient is too small.
- Bringing down two digits at once. Bring down one digit per step.
- Mixing up dividend and divisor. The dividend goes inside the bracket.
- Skipping the check. Multiply back to confirm the answer.
Frequently Asked Questions
Divide, multiply, subtract, then bring down the next digit. Repeat until no digits are left.
380 remainder 7, or about 380.5833.
Divide the remainder by the divisor. 7 ÷ 12 ≈ 0.5833, so 380 R 7 = 380.5833.
Put the remainder over the divisor. 380 R 7 is 380 7/12.
No. If it is, the quotient digit should be one higher.
Division by zero is undefined, so the calculator asks for a divisor of at least 1.
Multiply the quotient by the divisor and add the remainder. The result should equal the dividend.
Use the same steps, but look at enough digits of the dividend to fit the divisor at least once. Writing the divisor’s times table first makes each step faster.
Divide as normal and place the decimal point in the answer directly above the decimal point in the dividend.
Each digit stands for a place value. Bringing it down adds the next place to what is left, so you can keep dividing.
It is 0. For example, 96 ÷ 12 = 8 with no remainder.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Wikipedia, Long division | The long division method. | https://en.wikipedia.org/wiki/Long_division |
| Wikipedia, Euclidean division | Quotient and remainder. | https://en.wikipedia.org/wiki/Euclidean_division |