Long division calculator that shows every step: quotient and remainder, the decimal quotient with its repeating block marked, and the fraction.
By AdminDrafted with AI writing toolsUpdated Checked examples: 8
1,234 ÷ 7 = 176.(285714). The block 285714 repeats forever. The whole-number answer is 176 R 2, or 176 2/7 as a mixed number. R denotes the remainder.
| Step | Partial dividend | Quotient digit | Place | × 7 | Remainder |
|---|---|---|---|---|---|
| 1 | 12 | 1 | hundreds | 7 | 5 |
| 2 | 53 | 7 | tens | 49 | 4 |
| 3 | 44 | 6 | ones | 42 | 2 |
| 4 | 20 | 2 | tenths | 14 | 6 |
| 5 | 60 | 8 | hundredths | 56 | 4 |
| 6 | 40 | 5 | thousandths | 35 | 5 |
| 7 | 50 | 7 | ten-thousandths | 49 | 1 |
| 8 | 10 | 1 | hundred-thousandths | 7 | 3 |
| 9 | 30 | 4 | millionths | 28 | 2 |
Each line divides the current partial dividend by 7; the remainder, with the next digit brought down, starts the next line.
Multiply back and add the remainder to check the division.
After 0 decimal places, the same remainder returned 6 digits later, so the digits under the bar repeat forever.
Long division splits a division into one small division per digit. Take the leading digits of the dividend, divide by the divisor, write the digit above, multiply, subtract, then bring down the next digit and repeat. When the divisor has decimals, both numbers are first multiplied by the same power of 10 so the divisor is a whole number.
For 1234 ÷ 7 the working gives 176 with remainder 2, since 7 × 176 = 1232. Carrying on past the decimal point with appended zeros gives 176.285714…, and because the remainder 2 comes back after six more digits, the block 285714 repeats forever. The layout marks that block with a bar.
A fraction's decimal either ends or repeats. It ends when the reduced denominator has no prime factors other than 2 and 5, as with 487 ÷ 32 = 15.21875. Otherwise the length of the repeating block is the smallest k for which 10ᵏ − 1 is divisible by q once its factors of 2 and 5 are removed: 6 for q = 7 and 96 for q = 97.
Long division repeats four steps, one digit of the dividend at a time: divide, multiply, subtract, bring down. For 952 ÷ 4: 9 ÷ 4 = 2 remainder 1; bring down 5 to make 15, and 15 ÷ 4 = 3 remainder 3; bring down 2 to make 32, and 32 ÷ 4 = 8. So 952 ÷ 4 = 238.
Check any answer with divisor × quotient + remainder = dividend. Here 4 × 238 + 0 = 952.
When the divisor has two digits, take as many leading digits as it needs. For 487 ÷ 32, start with 48:
| Stage | Division digit | Product | Subtraction | Next step |
|---|---|---|---|---|
| Start with 48 | 1 | 1 × 32 = 32 | 48−32 = 16 | Bring down 7 to make 167 |
| Divide 167 | 5 | 5 × 32 = 160 | 167−160 = 7 | No original digits remain |
The answer is 15 remainder 7, checked by 32 × 15 + 7 = 487. As a mixed number, the remainder goes over the divisor: 15 7/32.
When a brought-down number is smaller than the divisor, the quotient digit is 0, and it must still be written. In 612 ÷ 6 the middle step is 1 ÷ 6 = 0, so the answer is 102, not 12. OpenStax Prealgebra sets out the whole-number method.
To keep going past the decimal point, write a point and zeros after the dividend and keep bringing them down. For 487 ÷ 32, the remainder 7 becomes 70, 60, 280, 240 and 160 in turn, giving the digits 2, 1, 8, 7 and 5, so 487 ÷ 32 = 15.21875 exactly.
A decimal ends when the reduced fraction's denominator has no prime factors other than 2 and 5. Since 32 = 2⁵, 7/32 ends. Otherwise a remainder must eventually repeat, and from then on the digits cycle.
For 1234 ÷ 7 = 176 remainder 2, the decimal part 2/7 is 0.285714285714…. Brackets mark the repeating block, so the answer is written 176.(285714).
A repeating decimal and a rounded one answer different questions: 1/3 is exactly 0.(3), while 0.33 is that value rounded to two places. For exact arithmetic with the remainder, use the fraction calculator.
Multiply both numbers by the same power of ten until the divisor is a whole number. For 4.71 ÷ 3.2, multiplying both by 10 gives 47.1 ÷ 32 = 1.471875. Moving the point in the divisor alone gives 4.71 ÷ 32 = 0.1471875, ten times too small.
A remainder stays in the original scale: 4.71 ÷ 3.2 is 1 remainder 1.51, because 3.2 × 1 + 1.51 = 4.71. The shifted division's remainder, 15.1, belongs to 47.1 ÷ 32. OpenStax's decimal operations explains why the shift leaves the quotient unchanged.
Period digits is the length of the repeating block, and 0 means the decimal ends.
| Division | Quotient/remainder | Decimal | Period digits |
|---|---|---|---|
| 1234 ÷ 7 | 176 R 2 | 176.(285714) | 6 |
| 487 ÷ 32 | 15 R 7 | 15.21875 | 0 |
| 4.71 ÷ 3.2 | 1 R 1.51 | 1.471875 | 0 |
| -17 ÷ 5 | −3 R −2 | −3.4 | 0 |
| 17 ÷ -5 | −3 R 2 | −3.4 | 0 |
| 0 ÷ 7 | 0 R 0 | 0 | 0 |
| 1 ÷ 3 | 0 R 1 | 0.(3) | 1 |
| 1 ÷ 97 | 0 R 1 | Continues… | 96 |
| 1 ÷ 8 | 0 R 1 | 0.125 | 0 |
The decimal for 1 ÷ 97 is marked as continuing because its repeating block is 96 digits long.
Truncating division, the convention used here, rounds the quotient toward zero and gives the remainder the dividend's sign: −17 ÷ 5 = −3 remainder −2, since 5 × (−3) + (−2) = −17. For 17 ÷ −5 the quotient is −3 and the remainder +2.
Floor division, the other common convention, gives −17 ÷ 5 = −4 remainder 3, since 5 × (−4) + 3 = −17.
Both satisfy dividend = divisor × quotient + remainder; they pick a different whole-number quotient, so use the one your course or programming language specifies.
Checked against: Independent calculation
Checked against: Calculator Soup long division tutorial: 487 ÷ 32 = 15 R 7
Checked against: Omni Calculator long division page: 65321 / 31 = 2107 r 4; period of 1/31 is 15
Checked against: Calculator Soup long division with decimals example (4.71 ÷ 3.2 = 1.471… to 3 places)
Repeat four moves: divide, multiply, subtract, bring down. For 487 ÷ 32: 48 ÷ 32 = 1, write 1, 1 × 32 = 32, 48 − 32 = 16; bring down 7 to make 167; 167 ÷ 32 = 5, 5 × 32 = 160, 167 − 160 = 7. No digits are left, so 487 ÷ 32 = 15 remainder 7. Check it: 32 × 15 + 7 = 487.
Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. For 4.71 ÷ 3.2, move both one place: 47.1 ÷ 32. The quotient stays the same because both numbers were multiplied by 10. Then divide as usual, putting the quotient's point directly above the dividend's: 47.1 ÷ 32 = 1.471875.
As a fraction, put the remainder over the divisor: 1234 ÷ 7 = 176 R 2 = 176 2/7. As a decimal, keep dividing: write a decimal point and zeros after the dividend and bring them down one at a time. 2/7 = 0.285714285714…, so 1234 ÷ 7 = 176.285714…, where the six digits 285714 repeat.
Watch the remainders. Once only appended zeros are being brought down, each step depends only on the current remainder, and there are fewer possible remainders than the divisor. As soon as a remainder appears a second time, the digits between the two appearances repeat forever. Dividing by 7 always repeats within 6 digits; 1 ÷ 97 has a 96-digit repeating block.
It depends on the convention. This page divides the absolute values and gives the remainder the dividend's sign, as C and Java do: −17 ÷ 5 = −3 R −2, since 5 × (−3) − 2 = −17; Excel's QUOTIENT truncates to −3 the same way. The floored convention used by Python's // and % and by Excel's MOD gives −4 R 3 instead, since 5 × (−4) + 3 = −17.
This calculator includes 8 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.