Long division calculator that shows every step: quotient and remainder, the decimal quotient with its repeating block marked, and the fraction.
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.
| 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.
The remainder came back 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.
Checked against: Python 3.8: divmod(1234, 7) = (176, 2); decimal.Decimal(1234) / 7 = 176.28571428571428571…; Fraction(1234, 7) = 1234/7
Checked against: Calculator Soup long division tutorial: 487 ÷ 32 = 15 R 7; 487/32 = 15.21875 by Python Fraction
Checked against: Omni Calculator long division page: 65321 / 31 = 2107 r 4; period of 1/31 is 15 (ord₃₁ 10 = 15, Python pow(10, 15, 31) == 1)
Checked against: Calculator Soup long division with decimals example (4.71 ÷ 3.2 = 1.471… to 3 places); exact 471/320 = 1.471875 and 4.71 − 3.2 = 1.51 by Python Fraction
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.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 8 worked examples whose answers come from independent sources; for example, “1234 ÷ 7 (default)” is checked against Python 3.8: divmod(1234, 7) = (176, 2); decimal.Decimal(1234) / 7 = 176.28571428571428571…; Fraction(1234, 7) = 1234/7.
Common Core State Standards for Mathematics, 6.NS.B.2 and 6.NS.B.3: divide multi-digit numbers and decimals using the standard algorithm; Hardy & Wright, An Introduction to the Theory of Numbers, §9.6 (period of a recurring decimal is the order of 10 modulo q); Wolfram MathWorld: Long division; Wolfram MathWorld: Repeating decimal.
8 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
Add, subtract, multiply and divide fractions and mixed numbers exactly, simplify to lowest terms, and convert decimals (including repeating) to fractions.
Calculate a mod n under the floored, truncated and Euclidean conventions, modular powers a^b mod m of large numbers, and modular inverses, with steps.
Round a number to decimal places, significant figures or the nearest ten or hundred under nine rules, including banker's rounding, floor and ceiling.
Scientific notation calculator: convert between decimal, scientific, E and engineering notation, and add, subtract, multiply or divide with sig-fig rules.
Factor calculator: every factor and factor pair of a whole number up to 10¹⁸, its prime factorization, divisor count and sum, and perfect or abundant.
Find X% of Y, what percent one number is of another, percentage increase or decrease, percent difference, and the original before a percentage was added.
Allow optional Google Analytics to measure page visits? Calculators work either way. Privacy and choices
Optional analytics: off.