Long division with remainders and every step shown.
This long division calculator shows every step of the long division method, the same way it is taught in school. Enter the number to be divided and the number to divide by, and you get the quotient and remainder, the answer as a decimal and as a mixed number, and a check that multiplies the answer back.
Quick answer: in long division, you divide one digit at a time from left to right. Divide, multiply, subtract, then bring down the next digit, and repeat. 7,835 ÷ 17 = 460 remainder 15, because 460 × 17 + 15 = 7,835.
How to Use the Long Division Calculator
- Enter the dividend, the number being divided, such as 7835.
- Enter the divisor, the number you are dividing by, such as 17.
- Read the quotient with its remainder, the decimal, the remainder, the mixed number, and the check.
- Follow the steps to see each bring-down.
The Parts of a Division
| Term | Meaning | In 7,835 ÷ 17 |
|---|---|---|
| Dividend | The number being divided | 7,835 |
| Divisor | The number you divide by | 17 |
| Quotient | The whole-number answer | 460 |
| Remainder | What is left over | 15 |
How to Do Long Division
Remember the steps with Divide, Multiply, Subtract, Bring down.
Example: 7,835 ÷ 17
- 17 does not go into 7, so look at 78. 17 goes into 78 4 times (4 × 17 = 68). 78 − 68 = 10.
- Bring down the 3 to make 103. 17 goes into 103 6 times (6 × 17 = 102). 103 − 102 = 1.
- Bring down the 5 to make 15. 17 goes into 15 0 times. The remainder is 15.
Answer: 460 R 15. As a decimal, 460.88235… As a mixed number, 460 15/17.
Check: 460 × 17 + 15 = 7,820 + 15 = 7,835. ✓
Writing the Remainder Three Ways
| Form | 7,835 ÷ 17 | When to use it |
|---|---|---|
| Remainder | 460 R 15 | Primary school answers, sharing whole objects |
| Mixed number | 460 15/17 | When the answer must be exact |
| Decimal | 460.882 (to 3 dp) | Money, measurements and most real-world answers |
What to Do With the Remainder in Word Problems
- Round up when everyone must be included: 130 people in cars that seat 4 need 33 cars, not 32 R 2.
- Round down when only complete items count: 130 cm of ribbon makes 4 full 30 cm pieces.
- Use the decimal for money: $130 shared by 4 people is $32.50 each.
Mistakes to Avoid
- Skipping a zero in the quotient. In 7,835 ÷ 17, the last step gives 0, so the answer is 460, not 46.
- A remainder bigger than the divisor. If it is, the step’s answer was too small. Go up by one.
- Forgetting to bring down a digit. Each digit of the dividend must be brought down once.
To turn a remainder into a repeating decimal, the fraction to decimal calculator shows the long division continuing past the decimal point.
Long Division FAQs
How do I check a long division answer?
Multiply the quotient by the divisor and add the remainder. You should get the dividend.
What if the divisor is bigger than the dividend?
The quotient is 0 and the remainder is the dividend. 5 ÷ 8 = 0 R 5, or 0.625 as a decimal.
Can I divide by a decimal?
Move the decimal point in both numbers until the divisor is a whole number. 7.5 ÷ 0.25 becomes 750 ÷ 25 = 30. This calculator works with whole numbers, so convert first.
How large can the numbers be?
The dividend can be up to 1 quadrillion (10¹⁵), and the divisor must be a positive whole number.
How we checked this page: the worked example was done by hand and matches the calculator’s steps, remainder, decimal and check.