Long Division Calculator
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1234 ÷ 7 = 176 R 2 = 176.(285714)
1234 ÷ 7 = 176 R 2 As a mixed number: 176 2/7 As a decimal: 176.(285714) (digits in brackets repeat) Check: 7 × 176 + 2 = 1234
| Step | Bring down | Divide | Multiply | Subtract | Quotient so far |
|---|---|---|---|---|---|
| 1 | – | 12 ÷ 7 = 1 | 1 × 7 = 7 | 12 − 7 = 5 | 1 |
| 2 | 3 | 53 ÷ 7 = 7 | 7 × 7 = 49 | 53 − 49 = 4 | 17 |
| 3 | 4 | 44 ÷ 7 = 6 | 6 × 7 = 42 | 44 − 42 = 2 | 176 |
| 4 | 0 | 20 ÷ 7 = 2 | 2 × 7 = 14 | 20 − 14 = 6 | 176.2 |
| 5 | 0 | 60 ÷ 7 = 8 | 8 × 7 = 56 | 60 − 56 = 4 | 176.28 |
| 6 | 0 | 40 ÷ 7 = 5 | 5 × 7 = 35 | 40 − 35 = 5 | 176.285 |
| 7 | 0 | 50 ÷ 7 = 7 | 7 × 7 = 49 | 50 − 49 = 1 | 176.2857 |
| 8 | 0 | 10 ÷ 7 = 1 | 1 × 7 = 7 | 10 − 7 = 3 | 176.28571 |
| 9 | 0 | 30 ÷ 7 = 4 | 4 × 7 = 28 | 30 − 28 = 2 | 176.285714 |
How to use the long division calculator
- Enter the dividend (the number being divided) and the divisor (the number you divide by). Decimals and negative numbers are allowed.
- Choose a decimal answer, or stop at the whole-number quotient and remainder as in early school exercises.
- Follow the steps table row by row; the last column shows the quotient growing one digit at a time. Copy the answer and check line from the box.
The long division method
Dividend = Divisor × Quotient + Remainder, with 0 ≤ remainder < divisor
Decimals: bring down zeros after the point; a remainder seen before means the digits repeat
Long division breaks a hard division into small ones. Start with the first part of the dividend that the divisor goes into, write how many times it goes (the next quotient digit), multiply back, subtract, and bring down the next digit to make a new number. When the digits run out, what is left is the remainder. To continue into decimals, put a decimal point in the quotient and keep bringing down zeros.
Each remainder is smaller than the divisor, so there are only a limited number of possible remainders. Once only zeros are being brought down, the moment a remainder appears for a second time, the digits from then on repeat. That is why every fraction is either a terminating or a repeating decimal, and it is how this calculator finds the repeating block, shown in brackets.
Worked example: 1234 ÷ 7
- 7 goes into 12 1 time: 1 × 7 = 7, 12 − 7 = 5.
- 7 goes into 53 7 times: 7 × 7 = 49, 53 − 49 = 4.
- 7 goes into 44 6 times: 6 × 7 = 42, 44 − 42 = 2.
- No digits are left, so the answer is 176 R 2, or 176 2/7 as a mixed number. Check: 7 × 176 + 2 = 1234.
- For decimals, bring down a 0: 7 goes into 20 2 times: 2 × 7 = 14, 20 − 14 = 6; 7 goes into 60 8 times: 8 × 7 = 56, 60 − 56 = 4; 7 goes into 40 5 times: 5 × 7 = 35, 40 − 35 = 5, and so on.
The remainders after the point run through every value from 1 to 6 before the first one comes back, so the six digits repeat: 1234 ÷ 7 = 176.(285714).
Dividing by a decimal
To divide 7.5 by 0.25, first move the decimal point 2 places to the right in both numbers so the divisor is a whole number: 7.5 ÷ 0.25 = 750 ÷ 25. Moving it the same distance in both keeps the answer the same, which is 30.
Unit fractions as decimals
| Division | Decimal | Pattern |
|---|---|---|
| 1 ÷ 2 | 0.5 | Terminates |
| 1 ÷ 3 | 0.(3) | Repeats every 1 digit |
| 1 ÷ 4 | 0.25 | Terminates |
| 1 ÷ 5 | 0.2 | Terminates |
| 1 ÷ 6 | 0.1(6) | Repeats every 1 digit |
| 1 ÷ 7 | 0.(142857) | Repeats every 6 digits |
| 1 ÷ 8 | 0.125 | Terminates |
| 1 ÷ 9 | 0.(1) | Repeats every 1 digit |
| 1 ÷ 10 | 0.1 | Terminates |
| 1 ÷ 11 | 0.(09) | Repeats every 2 digits |
| 1 ÷ 12 | 0.08(3) | Repeats every 1 digit |
| 1 ÷ 13 | 0.(076923) | Repeats every 6 digits |
Only divisors whose prime factors are 2 and 5 give terminating decimals. For a prime divisor p other than 2 and 5, the length of the repeating block always divides p − 1: it is 6 for 7 (which divides 6) and 2 for 11 (which divides 10).
Tips and common mistakes
- Keep the columns lined up. Write each quotient digit above the last digit of the number you just divided into.
- Don't skip zeros in the quotient. When the divisor doesn't go into the new number, write 0 and bring down the next digit; 618 ÷ 6 = 103, not 13.
- The remainder must be smaller than the divisor. If it isn't, the quotient digit was too small.
- Check by multiplying back: divisor × quotient + remainder should give the dividend.
- To turn the answer into a simplified fraction or do arithmetic with fractions, use the fraction calculator; for numbers with hundreds of digits, the big number calculator.
Frequently asked questions
How do you do long division?
Repeat four steps: divide, multiply, subtract, bring down. For 1234 ÷ 7: 7 goes into 12 once (12 − 7 = 5), into 53 seven times (53 − 49 = 4), into 44 six times (44 − 42 = 2), giving 176 remainder 2.
How do I write a remainder as a fraction or decimal?
Put the remainder over the divisor: 1234 ÷ 7 = 176 R 2 = 176 2/7. For a decimal, keep dividing by bringing down zeros: 176.285714285714…, written 176.(285714) because 285714 repeats.
How do I know when a decimal repeats?
Watch the remainders once you are bringing down only zeros. As soon as a remainder appears that you have seen before, the digits from that point repeat. For 1 ÷ 6, the remainder 4 keeps coming back, so 1 ÷ 6 = 0.1(6).
How do you divide by a decimal?
Move the decimal point to the right in both numbers until the divisor is a whole number, then divide as usual. 7.5 ÷ 0.25 becomes 750 ÷ 25 = 30.
What do the brackets in 0.(142857) mean?
The digits inside the brackets repeat forever: 0.(142857) = 0.142857142857… Some books draw a bar over the repeating digits instead; both notations mean the same thing.