Long Division Calculator
Perform long division with a bracket diagram and digit-by-digit steps. Get quotient with remainder plus exact decimal expansion.
Calculator
Number being divided
Non-zero divisor
0–20 places
Result: 100 ÷ 7
Step-by-Step Breakdown
| Step | Brought ↓ | Partial | Digit | Product | Rem. |
|---|---|---|---|---|---|
| 1 | 0 | 10 | 1 | 7 | 3 |
| 2 | 0 | 30 | 4 | 28 | 2 |
| 3 (dec) | 0 | 20 | 2 | 14 | 6 |
| 4 (dec) | 0 | 60 | 8 | 56 | 4 |
| 5 (dec) | 0 | 40 | 5 | 35 | 5 |
| 6 (dec) | 0 | 50 | 7 | 49 | 1 |
| 7 (dec) | 0 | 10 | 1 | 7 | 3 |
| 8 (dec) | 0 | 30 | 4 | 28 | 2 |
Results
Quotient (with Remainder)
14 R 2
Integer result plus leftover
14.285714
To 6 decimal places
2
Less than |7|
8
Integer + decimal rows
14
Digits above the bracket
100
Should equal the dividend (integer part)
Digit-by-digit long division; integer rows exact, decimal tail exact to the requested 0–20 places. Verify with divisor × quotient + remainder.
Visualizations
Quotient Digits
Integer vs Decimal Steps
Remainder Progress
Remainder vs Divisor
Formula
Each row isolates one quotient digit: floor the partial dividend by the divisor, subtract the product, and append the next digit (or zero past the point). The integer rows give q with remainder; decimal rows extend q past the point.
Alternative Form
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| a | Dividend | integer | Inside the bracket |
| b | Divisor | integer | Outside-left, non-zero |
| q | Quotient | number | Above the bracket |
| r | Remainder | integer | Leftover, always < |b| |
| p | Precision | digits | Decimal places (0–20) |
Explanation
Long division is repeated Euclidean reduction: every row replaces the partial dividend with its remainder, shrinking the problem one digit at a time.
Derivation
Row: qᵢ = ⌊m/b⌋, m ← 10·(m − qᵢb) + next digit. Integer rows consume dividend digits; decimal rows consume zeros. Stop at p places or r = 0.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Set up 100 ÷ 7: divisor outside-left, dividend inside the bracket.
Take the leading digits until the partial dividend reaches the divisor; the first quotient digit follows.
Multiply, subtract, and bring down the next digit — the DMSB cycle.
For decimals, point the quotient and bring down zeros.
Stop at precision or a zero remainder (terminating) vs a cycle (repeating).
Verify with the division algorithm.
Worked Examples
See how the calculator works with different scenarios.
Scenario
Default split-bill style division.
Inputs
Calculation
7 into 10 → 1 (r3); bring 0 → 30 → 4 (r2); decimals → 285714…
Result
14 R 2 = 14.285714
Interpretation
Repeating 285714 cycle; remainder 2 = 2/7 of a unit.
Understanding Your Result
Your Result: Quotient (with Remainder): 14 R 2
Typical range: Remainders 0–|b|−1; decimal tails terminate or cycle within b−1 digits.
What This Means
Quotient+R is the whole-unit answer; the decimal form is the same value extended past the point; remainder < |divisor| certifies correctness.
Why It Matters
Per-unit costs, averages, rates and conversions are all long division; the step table teaches estimation and place value.
Professional Interpretation
Read integer rows for grouping, decimal rows for measurement; always confirm a = b·q + r.
Recommendations
- •Estimate each digit by rounding b
- •Keep columns aligned (graph paper helps)
- •Multiply back after each row
- •Watch leading-zero place values
- •Name repeating cycles with a bar
Educational Content
Introduction
Division splits a dividend into divisor-sized groups. Long division mechanizes the split one digit at a time with a fixed four-move cycle.
Concept Explanation
Partial dividend → quotient digit → product → remainder → bring down. Decimals append zeros; signs follow positive÷negative = negative.
Applications
Benefits
- •Exact integer accountability
- •Teaches place value deeply
- •Self-checking via multiply-back
- •Handles any digit length
- •Reveals terminating vs repeating structure
Limitations
- •Manual estimation on multi-digit b
- •No fractional divisor entry here
- •Precision capped at 20 places
- •ASCII bracket is schematic
Best Practices
- •Master ×12 tables for estimation
- •Round b to estimate digits
- •Verify a = b·q + r every time
- •Track the decimal point strictly
- •Use the step table to find slips
Common Misconceptions
Practical Tips
- •Say DMSB each row: divide, multiply, subtract, bring down
- •Estimate digits by rounding the divisor
- •Keep digits column-aligned
- •Multiply back to verify each row
- •Write 0 placeholders, never skip
- •Add zeros deliberately for decimals
- •Stop and name cycles instead of over-typing
Common Mistakes
Assumptions
This calculator makes the following assumptions to provide estimates:
Limitations
Be aware of these limitations when using this calculator:
Frequently Asked Questions
Answers to common questions about this calculator.
What is long division?
What are the steps of long division?
What is the difference between dividend, divisor, quotient and remainder?
What does R mean in division results?
Can a remainder be larger than the divisor?
What happens when the divisor exceeds the dividend?
What is a terminating vs repeating decimal?
What is the division algorithm?
Can you divide by zero?
How do you check long division answers?
How do you handle decimals in long division?
Why is long division still taught with calculators available?
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Related Guides
Deepen your understanding with these educational resources.
Glossary
Technical terms used in mortgage calculations explained in plain language.
- Dividend
- Number divided; inside the bracket.
- Divisor
- Number dividing; outside-left.
- Quotient
- Result; digits above the bracket.
- Remainder
- Leftover with 0 ≤ r < |b|.
- Partial dividend
- Working value at each row.
- Terminating decimal
- Finite tail ending at r = 0.
- Repeating decimal
- Cycling tail (vinculum/bar).
- Bus-stop method
- Short division; mental subtract steps.
- Division algorithm
- a = bq + r existence/uniqueness.
- Chunking
- Subtracting large multiples instead of digits.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
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Page Information
2026-08-07
2.0.0
Free to use for educational and professional purposes.