Long Division Calculator

Use this Long Division Calculator to compute accurate results with a clear, step-by-step long division breakdown. Choose Remainder (R form) for classic quotient-and-remainder output, or switch to Decimal mode to generate digits precisely. If you need a simpler tool, try the Division Calculator. For probability help, explore the binomial distribution calculator. You can also browse more tools in Math Calculators.

Calculate long division

Exact integer math for quotient/remainder and remainder-based digit generation for decimals.

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Results

Quotient and remainder are always computed. Decimal appears in Decimal mode.

Quotient (Q)

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Integer division truncates toward zero.

Remainder (R)

—

Remainder follows the dividend sign.

Division Completion (Exactness) —

This indicator compares the remainder size to the divisor: remainder 0 means an exact division (100%).

Step-by-step long division breakdown

Accuracy & Method

This calculator runs locally in your browser using exact integer math for quotient/remainder and remainder-based digit generation for decimals. That means the quotient and remainder are computed with BigInt, and decimals are produced by repeatedly multiplying the remainder by 10, then taking the next digit—similar to how long division is taught on paper.

Rounding/Precision Policy

In Decimal mode, digits are truncated to your selected precision (0–12). Truncation means we stop after generating the chosen number of digits and do not round the last digit up. If precision is 0, the output shows only the integer part (no decimal point).

Privacy-first

Your inputs never leave your device. Everything is computed in-page without sending data to a server.

Last updated: 2026-01-13

Sources & References

  • Standard long division method
  • Integer division identity A = B×Q + R
  • Remainder-based digit generation for decimals
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How it works

Let the Dividend be A and the Divisor be B (with B ≠ 0). The calculator finds the Quotient Q and Remainder R such that:

A = B×Q + R

The remainder is constrained by magnitude: 0 ≤ |R| < |B|. In this calculator, the remainder follows the sign of the dividend (A), which is the common behavior in many programming languages when using integer division and modulo with truncation toward zero.

BigInt division truncates toward zero, meaning 7 ÷ 2 = 3 remainder 1, and -7 ÷ 2 = -3 remainder -1. This matches the identity above and keeps the output consistent across positive and negative inputs.

In Decimal mode, the integer part is computed first using exact integer division. Then decimal digits are generated by repeating: multiply the absolute remainder by 10, take the next digit by dividing by |B|, and keep the new remainder for the next digit. This avoids floating-point rounding issues because every digit is produced through exact integer math. Decimal digits are truncated to the chosen precision.

Use cases

  • Homework long division checks: verify each subtraction and bring-down step.
  • Converting a fraction to a decimal: switch to Decimal mode for controlled precision.
  • Splitting costs evenly and tracking remainder: see what’s left over after equal shares.
  • Verifying exact divisibility: a remainder of 0 confirms a clean division.
  • Quick sanity checks for large integers: compute quotient/remainder without rounding errors.

Examples

Example 1: 125 ÷ 4

Inputs: Dividend 125, Divisor 4
Remainder mode output: Quotient = 31, Remainder = 1 → Result: 31 R 1
Decimal mode (precision 6): 31.250000 (truncated to 6 digits).

Example 2: 1000 ÷ 16

Inputs: Dividend 1000, Divisor 16
Remainder mode output: Quotient = 62, Remainder = 8 → Result: 62 R 8
Decimal mode (precision 6): 62.500000.

Example 3: -45 ÷ 6

Inputs: Dividend -45, Divisor 6
Remainder mode output: Quotient = -7, Remainder = -3 → Result: -7 R -3
Decimal mode (precision 6): -7.500000. The sign follows the quotient sign, and the remainder follows the dividend sign.

Common Mistakes

  • Dividing by 0: the divisor cannot be 0.
  • Entering decimals in inputs: this tool accepts integers only (no decimal points).
  • Forgetting negative sign rules: quotient sign depends on A and B, remainder follows A.
  • Confusing remainder with decimal part: remainder mode shows leftover; decimal mode extends digits.
  • Misplacing zeros in quotient: long division can require zeros when bringing down digits.

Quick Tips

  • Use Remainder mode for huge integers when you mainly need Q and R quickly.
  • Increase precision when you need more decimal digits for a fraction-like result.
  • Check exactness via remainder 0: it confirms the division is exact.
  • Use the steps to verify each subtraction and make sure you brought down the right digit.
  • Copy summaries for notes or homework: they include inputs, mode, and key outputs.

FAQ

What is long division?
Long division is a step-by-step method for dividing one number by another by repeatedly taking the largest multiple of the divisor that fits into the current portion of the dividend. You “bring down” digits one at a time, divide to get a quotient digit, multiply the divisor by that digit, subtract, and continue until no digits remain. The final result is an integer quotient and a remainder, or you can keep extending the result into decimal digits by continuing the process after the last digit using remainder × 10.
How do I interpret the remainder (R form)?
Remainder form shows the result as “Q R R,” meaning quotient Q with remainder R. For example, 125 ÷ 4 = 31 R 1 tells you that 4 goes into 125 exactly 31 times, and 1 is left over. This is especially useful when the answer needs to stay in integer terms, such as grouping items evenly or checking divisibility. You can always rebuild the dividend with the identity A = B×Q + R to confirm the result.
Why does the remainder sometimes have the same sign as the dividend?
This calculator uses integer division that truncates toward zero, which is a common rule in many programming languages. Under this rule, the quotient is the truncated integer result, and the remainder is what is left so that A = B×Q + R remains true. When A is negative, the leftover portion R also becomes negative to keep the identity consistent. This sign policy keeps results predictable and avoids mixing sign rules between the quotient and the remainder.
Can this Long Division Calculator handle very large integers?
Yes. The core calculations use BigInt, which supports very large integer values beyond typical 32-bit or 64-bit limits. Inputs are treated as strings first, validated as strict integers, and then converted to BigInt for exact division and modulo operations. Decimal digits are generated using repeated integer operations rather than floating-point math. For extremely long numbers, the calculator may limit the step-by-step display to keep the page fast, but it will still compute the main results.
How does decimal mode create digits without rounding errors?
Decimal mode avoids floating-point arithmetic by producing digits the same way you would by hand. After computing the integer quotient and remainder, it repeatedly multiplies the remainder by 10, divides by the absolute divisor to get the next digit, then updates the remainder. Each step is exact because it uses integer operations only. As a result, you don’t get binary floating-point artifacts like 0.30000000000000004. The displayed decimal is built digit-by-digit with precise control.
What does the precision setting do in decimal mode?
Precision controls how many digits appear after the decimal point, from 0 to 12. If you choose precision 0, the calculator shows only the integer part, which can be useful when you want truncation to an integer. With higher precision, the calculator generates more digits by continuing the remainder × 10 process. This tool truncates rather than rounds, meaning it stops once it has generated the selected number of digits and does not adjust the last digit upward.
Why might my step-by-step breakdown be limited for extremely long numbers?
Step-by-step long division can require one full set of operations per digit of the dividend, plus additional steps for decimal extension. If you enter a dividend with hundreds or thousands of digits, creating a very large step list can slow down the page or make it difficult to read. To keep the tool responsive, the calculator limits step generation when the dividend is extremely long. Even when steps are limited, the quotient, remainder, and decimal digits (up to your chosen precision) are still computed exactly.
What’s the difference between long division and a standard division calculator?
A standard division calculator often focuses on the final numeric answer and may default to decimals with floating-point rounding. Long division emphasizes the process: dividing digit-by-digit, multiplying, subtracting, and bringing down digits to form a quotient and remainder. This tool provides both: a classic quotient-and-remainder output plus an optional decimal expansion built from the remainder process. It’s especially useful when you want to verify each step, confirm exactness, or work with very large integers where floating-point results might be misleading.

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