Each row shows the partial dividend considered, the largest multiple of the divisor subtracted, the new remainder,
and the next digit brought down. When decimal places are requested, zeros are brought down after the decimal point.
#
Partial dividend
Subtract (mult × divisor)
Remainder
Bring down
Long Division – Quick Cheat Sheet
Vocabulary:Dividend ÷ Divisor = Quotient, remainder R.
Process: Compare the leftmost digits of the dividend to the divisor, find the largest multiple that fits, subtract, bring down the next digit, and repeat.
Decimals: After the integer digits are exhausted, append zeros and continue for the requested decimal places.
Sign: The quotient sign is negative if exactly one of (dividend, divisor) is negative; remainder follows the dividend’s sign.
Validation: Divisor must be non-zero. Only numeric input is accepted (decimals are rounded to integers first).
Check:divisor × quotient + remainder should match the original dividend (for the integer portion used).
Edge cases & notes
If the divisor is larger than the dividend, the integer quotient is 0; the remainder is the dividend.
With decimals requested, we extend the algorithm by “bringing down” zeros after the decimal point.
This tool rounds any decimal input to the nearest integer before running long division (classic board method).
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