Long Division Calculator

How to use the long division calculator

1. Type the Dividend (number to divide) and the Divisor (number to divide by). Whole numbers of any length work, as do decimals such as 12.5 or 0.25 and negative numbers.
2. Choose the number of Decimal places. With 0, the division stops at the whole-number quotient and gives a remainder, as in primary school. With 2, 5 or up to 50, zeros are added after the point and the division continues until the remainder is 0 or the places are written.
3. Pick a Layout: US bracket (divisor on the left) or French potence (divisor on the right). Untick Write the subtractions to show only the successive remainders, as many European pupils do once they are confident.
4. The results update as you type (or click Divide). You get the Quotient and remainder, the exact Decimal result with the repeating block in brackets, the value rounded to your number of places, and a Check line that multiplies back.
5. Below, the written division is drawn digit by digit, the Step by step list explains every move in words, and Divisibility notes apply the classic tests to the dividend. Copy layout as text copies the drawing for a message or a document.

How long division works

Long division splits a big division into small ones you can do in your head. Take the first digits of the dividend that make a number at least as large as the divisor, and ask how many times the divisor fits: that is the first digit of the quotient. Multiply, subtract, and bring down the next digit next to the remainder. Repeat until every digit is used. For 125 ÷ 3: 12 ÷ 3 = 4 (12 − 12 = 0), bring down 5, 5 ÷ 3 = 1 (5 − 3 = 2). The answer is 41 remainder 2, and indeed 3 × 41 + 2 = 125.

To go past the decimal point, write a point in the quotient, add a 0 to the remainder and keep dividing: 20 ÷ 3 = 6 remainder 2, again and again, so 125 ÷ 3 = 41.666… The calculator notices when a remainder comes back: from that moment the digits repeat forever, and it marks the repeating block (underlined in the layout, in brackets in the result, e.g. 41.(6)).

When the divisor has decimals, the tool first moves the point in both numbers the same number of places, which does not change the quotient: 12.5 ÷ 0.25 becomes 1250 ÷ 25 = 50.

Two ways to write it

In the United States, the United Kingdom and Canada, the divisor sits to the left of a bracket, the dividend under a bar, and the quotient on top, each digit above the column it belongs to. In France, Belgium, Quebec schools and much of Europe, the “potence” puts the dividend on the left, the divisor on the right of a vertical line, and the quotient under the divisor. The arithmetic is exactly the same; only the placement changes.

Remainders, negatives and divisibility

With negative numbers, the division is done on the absolute values and the sign is applied afterwards. The remainder shown has the sign of the dividend (−17 ÷ 5 = −3 remainder −2), as most calculators and programming languages do; the notes also give the Euclidean form, where the remainder is never negative (−4 remainder 3).

A fraction written in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5; otherwise the decimal repeats. For a whole-number dividend, the notes apply the quick tests: last digit for 2, 5 and 10, last two digits for 4, last three for 8, digit sum for 3 and 9, both 2 and 3 for 6, and the alternating digit sum for 11.