Long Division Calculator
Enter the two numbers and this sets out the division the way it would be written on paper — one digit at a time, with the remainder carried across.
Answer
1,350remainder 2
- Quotient
- 1,350
- Remainder
- 2
- As a fraction
- 1,350 and 2/7
- As a decimal
- 1,350.29
- Check
- 1,350 × 7 + 2 = 9,452
- Step 1 — bring down the 9 to make 9. 7 goes into 9 1 time, which is 7. Take it away and 2 is left.
- Step 2 — bring down the 4 to make 24. 7 goes into 24 3 times, which is 21. Take it away and 3 is left.
- Step 3 — bring down the 5 to make 35. 7 goes into 35 5 times, which is 35. Take it away and 0 is left.
- Step 4 — bring down the 2 to make 2. 7 goes into 2 0 times, which is 0. Take it away and 2 is left.
- There is 2 left over, which is the remainder. It is always smaller than the number you are dividing by.
About long division
Long division breaks a big division into a run of small ones. Instead of asking how many sevens are in 9,452 all at once, you work across the digits from the left, dividing what you have so far and carrying whatever is left over into the next column.
Each step is the same four actions: divide, multiply, subtract, bring down. Divide what you are holding by the divisor, multiply the answer back to see how much that accounted for, subtract to find what is left, then bring down the next digit and go again.
Two things trip people up. The first is a zero in the middle of the answer — if the divisor does not go into what you are holding, the quotient gets a 0 in that column and the whole amount carries forward. Dropping that zero is the most common way to get an answer that is a factor of ten out.
The second is the remainder. It is what is left when there are no digits to bring down, and it is always smaller than the number you divided by — if it is not, the last step took too little. Multiplying the quotient back by the divisor and adding the remainder should give exactly the number you started with, which is the check shown alongside every answer here.
What it works out
- Quotient and remainder
- Every step of the written method
- The multiplication check
- The answer as a decimal
The formula
Divide, multiply, subtract, bring down — then repeat Check: Quotient × Divisor + Remainder = Dividend
Working across 9,452 divided by 7, one digit at a time.
Bring down the 9. Seven goes into 9 once, which is 7, and 2 is left. Bring down the 4 to make 24. Seven goes into 24 three times, which is 21, and 3 is left. Bring down the 5 to make 35. Seven goes into 35 five times exactly, and nothing is left. Bring down the 2. Seven does not go into 2 at all, so that column gets a 0 and the 2 stays.
Reading the digits down the quotient gives 1,350, with 2 left over.
The zero in that last step is the one to watch. It has to be written — the answer is 1,350 and not 135 — and skipping it because "seven does not go into two" is how this goes wrong.
Check it by multiplying back: 1,350 × 7 is 9,450, plus the remainder of 2 makes 9,452. If that does not return the number you started with, one of the steps is wrong, and comparing the steps shows which.
- Dividend
- The number being divided — the one that goes under the bracket.
- Divisor
- The number you are dividing by — the one outside.
- Quotient
- The answer that builds up along the top, one digit per step.
- Remainder
- What is left at the end. Always smaller than the divisor.
A worked example
9,452 divided by 7.
That works out to 1,350 remainder 2.
- Quotient
- 1,350
- Remainder
- 2
- As a fraction
- 1,350 and 2/7
- As a decimal
- 1,350.29
- Check
- 1,350 × 7 + 2 = 9,452
Questions
How do you do long division?
Four steps repeated: divide, multiply, subtract, bring down. Take the digits from the left one at a time, divide what you are holding by the divisor, and carry whatever is left into the next column.
What is 9452 divided by 7?
1,350 remainder 2, or 1,350.2857 as a decimal. Checking it back: 1,350 × 7 = 9,450, plus 2 makes 9,452.
What if the divisor does not go into a digit?
That column gets a 0 in the answer and the whole amount carries to the next digit. The zero must be written down — leaving it out is the most common mistake in long division and puts the answer out by a factor of ten.
What is a remainder?
What is left over when the division will not go exactly. It is always smaller than the divisor — if you end up with a remainder as big as the number you are dividing by, the last step took too little.
How do I check a long division?
Multiply the quotient by the divisor and add the remainder. That should give back the number you started with exactly. It is a quick check and it catches almost every slip.
How do I turn a remainder into a decimal?
Put a decimal point in the answer, add a zero to the remainder and carry on dividing. A remainder of 2 divided by 7 becomes 20 ÷ 7, and the digits continue from there.
Why is long division taught when calculators exist?
Because the method is the point rather than the answer. It builds place value, estimation and the habit of checking, and the same structure reappears later in dividing polynomials.
What are the parts of a division called?
The dividend is the number being divided, the divisor is what you divide by, the quotient is the answer and the remainder is what is left.