Long Division Calculator With Steps & Remainders

Long division on paper—and on screen

Long division is the standard written algorithm for dividing large numbers: at each step you ask how many times the divisor fits into the current partial dividend, multiply, subtract, and bring down the next digit. The integer phase ends with a quotient Q and remainder R satisfying Dividend = Divisor × Q + R with 0 ≤ R < |Divisor|. Continuing the process after the decimal point appends zeros to the remainder and produces decimal digits; if a remainder value repeats, the decimal repeats forever and we mark the repeating block (for example 1 ÷ 3 = 0.(3) and 2/7 = 0.(285714)). When either input has a decimal point, multiply both numbers by the same power of ten so the divisor becomes an integer—shifting the point does not change the true quotient—then run the same algorithm. This calculator shows Q and R, a decimal form with parentheses around repeating digits, an aligned monospace layout similar to classroom scratch work, and numbered text steps. It is complementary to a remainder-only modulo tool: use long division when you need the full written process or a decimal expansion, and the remainder calculator when you only need R.

Required Inputs & Typical Use Cases

Check homework long-division problems, convert improper results into decimals with clear repeating notation, explain why 100 ÷ 8 equals 12.5, or diagnose division-by-zero mistakes before they show up in spreadsheets.

The Formula

Dividend = Divisor × Quotient + Remainder
0 ≤ Remainder < |Divisor|
Decimal digits from repeated (remainder × 10) ÷ divisor

• Dividend

  Number being divided

• Divisor

  Number you divide by (must be non-zero)

• Quotient

  Whole-number result of the integer division

• Remainder

  Leftover after the integer quotient

Worked Example

1. 1234 ÷ 7

   Quotient 176 remainder 2, since 7×176 + 2 = 1234. Decimal 176.(285714) with repeating block 285714.

2. 100 ÷ 8

   12 R 4, and the decimal terminates as 12.5.

3. 1 ÷ 3

   0 R 1 → 0.(3).

Tips, Assumptions & Limitations

• Choose enough decimal places to reveal a repeating cycle when you expect one.
• Comma-separated thousands (1,234) are accepted in the inputs.
• Division by zero always errors—there is no quotient to display.
• Common mistake: writing the remainder larger than the divisor.
• Common mistake: shifting only one decimal point when both inputs have decimals.
• For polynomial division, see the synthetic division calculator instead.