Long Division Calculator - Quotient, Remainder, and Steps

A long division calculator computes dividend ÷ divisor the way a classroom tableau does: one digit of the dividend at a time, a quotient digit, a product, a subtraction, and a remainder that becomes the next working value when the following digit is brought down. The output is not only a decimal on a calculator screen. You get the integer quotient, the remainder (strictly smaller than the divisor), and - if you ask for them - extra digits after the decimal point obtained by bringing down zeros.

That layout exists because division is the inverse of multiplication with a leftover. For whole numbers, dividend = quotient × divisor + remainder, with 0 ≤ remainder < divisor. 847 ÷ 5 is 169 remainder 2 because 169 × 5 + 2 = 845 + 2 = 847. If you continue past the ones place, those leftover 2 ones become 20 tenths, which 5 goes into 4 times, and so on. A four-function calculator hides that story; this page prints it.

This free online division tool with steps accepts non-negative numbers, including a single decimal point in the dividend or divisor. Both values are scaled to integers by the same power of ten (at most eight extra fractional digits) so the algorithm stays in exact integer arithmetic. Repeating decimals such as 22 ÷ 7 are truncated at the place count you choose - this page does not draw a repeating bar. Arithmetic after the page loads stays in your browser.

The quotient and remainder calculator is meant to sit next to a homework page:

1. Enter the dividend (the number being split) and a non-zero divisor. Whole numbers are used as-is. Decimals such as 12.5 and 2.5 are scaled together (125 and 25) before the tableau runs.
2. Choose decimal places: 0 keeps a whole-number remainder; 2, 4, 6, 8, or 12 continue the division by bringing down zeros after the decimal point. The extra digits are cut off at that count, not rounded.
3. Read the quotient, the remainder after the integer digits, the check identity, the monospace tableau, and the step table (bring down, working value, quotient digit, product, remainder).
4. Copy the summary or clear the fields. The last dividend, divisor, and place count are stored locally for up to 30 days.

Note: negatives are rejected. Division by zero is rejected. If you need a chain of operations rather than a single division, use the basic calculator.

For each digit of the (scaled) dividend, and then for each extra zero you requested after the decimal point:

1. Bring down the next digit.
2. Form the working value: current remainder × 10 + that digit.
3. The next quotient digit is floor(working value ÷ divisor).
4. Subtract (quotient digit × divisor) from the working value. That difference is the new remainder.

If the working value is still smaller than the divisor, the quotient digit is 0 and you simply bring down another digit - the same thing you do on paper when the first digit of 22 ÷ 7 is too small and you look at 22 instead.

Default fields on this page are 847 and 5 because the division is short, exact as an integer-plus-remainder problem, and clean when you continue into tenths. Integer division first.

• Bring down 8. Working value 8. 8 ÷ 5 = 1. Product 5. Remainder 3.
• Bring down 4. Working value 34. 34 ÷ 5 = 6. Product 30. Remainder 4.
• Bring down 7. Working value 47. 47 ÷ 5 = 9. Product 45. Remainder 2.

Quotient digits 1, 6, 9 give 169. Remainder 2. Check: 169 × 5 + 2 = 845 + 2 = 847. In words: five goes into eight hundred forty-seven one hundred sixty-nine times, with two left over.

Set decimal places to 2 and the algorithm keeps going with zeros:

• Bring down 0. Working value 20. 20 ÷ 5 = 4. Product 20. Remainder 0.
• Bring down 0. Working value 0. 0 ÷ 5 = 0. Product 0. Remainder 0.

The truncated expansion is 169.40. Here the remainder hit zero, so the decimal terminates; two places simply show a trailing zero. Many homework keys still want 169 r 2 rather than 169.4, which is why place count 0 is the default.

22 ÷ 7 is the classic “it never ends” example. Integer division is still finite: 7 goes into 22 three times because 3 × 7 = 21, remainder 1. Check: 3 × 7 + 1 = 22.

• Bring down 2. Working value 2. 2 ÷ 7 = 0. Product 0. Remainder 2 (the first digit is too small).
• Bring down 2. Working value 22. 22 ÷ 7 = 3. Product 21. Remainder 1.

Continue with four decimal places by bringing down zeros:

• Bring down 0 → 10. 10 ÷ 7 = 1, product 7, remainder 3.
• Bring down 0 → 30. 30 ÷ 7 = 4, product 28, remainder 2.
• Bring down 0 → 20. 20 ÷ 7 = 2, product 14, remainder 6.
• Bring down 0 → 60. 60 ÷ 7 = 8, product 56, remainder 4.

The truncated quotient is 3.1428. The true expansion 3.142857142857… repeats the block 142857. This calculator does not detect or mark the repeat; it stops at the number of places you selected. If a key wants 3.14, choose 2 places and you get 3.14 by truncation (the next digit would have been 2, so rounding to two places would also be 3.14 in this particular case, but 1 ÷ 6 to two places truncates to 0.16 while rounding would give 0.17). Always match your teacher’s rounding rule separately.

When the inputs already contain a decimal point, the remainder after the integer stage is a remainder of the scaled integers. 12.5 ÷ 2 with 0 extra places scales to 125 ÷ 20 = 6 remainder 5, which is 6 remainder 0.5 in the original units because the scale was 10¹. The result panel prints both the scaled remainder and the original units when a scale was applied.

Place-value language helps when a student is lost in the tableau. In 847 ÷ 5, the 1 is hundreds of fives, the 6 is tens of fives, and the 9 is ones of fives. The leftover 2 ones become 20 tenths if you continue, which is why the first decimal digit is 4. In 22 ÷ 7 the leftover 1 one becomes 10 tenths, and 7 fits once, leaving 3 tenths, which become 30 hundredths, and so on through 3.1428. That story is the same algorithm as the table; it is only the units that change when you cross the decimal point.