How this calculator works
- Step 1Bring downnext digitAttach the next digit to the remainder.
- Step 2Dividehow many timesFind how many times the divisor fits.
- Step 3Multiply, subtractnew remainderTake that much away and carry on.
Long division repeats one small step for each digit. After the last digit, adding a decimal point and zeros carries the division on into decimals.
Worked example: 7894 ÷ 13
- Each step
current = remainder × 10 + next digit
- 7813 × 6 = 78remainder 0
- 913 × 0 = 0remainder 9
- 9413 × 7 = 91remainder 3
- 30 (after the point)13 × 2 = 26remainder 4
- 40 (after the point)13 × 3 = 39remainder 1
- Answer607 remainder 3
As a decimal it is 607.(230769): the block 230769 repeats for ever.
Ending or repeating
- 1 ÷ 80.125Ends: 8 has only the prime 2.
- 1 ÷ 60.1(6)One digit, then a repeat.
- 1 ÷ 70.(142857)Six digits repeat for ever.
A decimal ends only when the divisor, after cancelling, has no prime factors other than 2 and 5.
Assumptions and limits
- Whole numbersDividend up to 10¹⁵, divisor up to 10⁹.
- Exact decimalRepeating blocks are found exactly.
- Up to 10 placesSteps can continue past the point.
- Long cyclesBlocks over 300 digits are cut short.
Related number tools
Long division gives a quotient and remainder. Fractions and rounding are the next steps.
To simplify the result as a fraction, use the fraction calculator. For a decimal to a set number of places, try the rounding calculator.
Common mistakes
Mistake: Forgetting a 0 in the quotient.
Instead: Write 0 when the divisor does not fit.
Mistake: Leaving a remainder bigger than the divisor.
Instead: The divisor could fit once more.
Mistake: Rounding 0.(3) to 0.33 as exact.
Instead: Use brackets or say “about 0.33”.
Checking the method
A separate script re-works every golden value with divmod and number theory, without watching remainders.
Read how we test our calculators, or browse more maths calculators.