How to use this calculator
- Enter or choose dividend (number being divided).
- Enter or choose divisor.
- The answer updates as you type. Use Copy result or Share to keep it.
Method
Dividend = Divisor × Quotient + Remainder, with 0 ≤ Remainder < Divisor
- Dividend
- the number being divided
- Divisor
- the number you divide by
Worked example
- 10 ÷ 7 = 1, remainder 3; bring down 0 to make 30.
- 30 ÷ 7 = 4, remainder 2; bring down 0 to make 20.
- 20 ÷ 7 = 2, remainder 6. Quotient 142, remainder 6; check: 7 × 142 + 6 = 1000.
1000 ÷ 7 = 142 remainder 6, which is 142 6/7 or 142.857142857… with 857142 repeating.
What the result means
The remainder is what is left over after sharing out equally. Every fraction gives a decimal that either ends or repeats; the repeating block, shown in brackets, is written with a bar over it in many textbooks.
Assumptions and limits
- Whole-number dividend from 0 to 10¹⁵ and divisor from 1 to 10⁹.
- Repeating blocks longer than 1,000 digits are cut off and marked.
Questions
How do I check a long division?
Multiply the quotient by the divisor and add the remainder. You should get the dividend back.
Why does 1/7 repeat with six digits?
There are only six possible non-zero remainders when dividing by 7, so the remainders, and therefore the digits, must start repeating within six steps.