Example: Remainder mode (default) → 127 ÷ 5 = 25 R 2
Dividend 127, divisor 5, Quotient with remainder. Quotient 25, remainder 2. Show your work walks each cycle left to right through the digits.
Long division with steps
Long Division Calculator: Remainder or Decimal
This calculator performs long division on non-negative integers and returns either a quotient with remainder or a decimal to n places. Each run lists annotated DMSB steps (divide, multiply, subtract, bring down) in Show your work. Valid results satisfy with . Divisor must be greater than zero. It does not handle fractions, negative numbers, or polynomial long division.
By Jeff Beem
Updated
Dividend & divisor
Non-negative integers only. Default example: 127 ÷ 5.
Result
Quotient25
Remainder2
127 ÷ 5 = 25 R 2
Show your work
Each step: divide, multiply, subtract, bring down.
5 goes into 12 2 times; 2 × 5 = 10
12 − 10 = 2 → bring down 7
5 goes into 27 5 times; 5 × 5 = 25
27 − 25 = 2
How to use this calculator
Enter Dividend (n) and Divisor (d) (d > 0). Pick Quotient with remainder or Decimal result (set decimal places when needed). Read quotient and remainder on the dark panel; scroll Show your work for each DMSB step.
Reading your long division result
The dark result panel shows quotient (and remainder in remainder mode). Show your work lists annotated DMSB steps. Pick the result type your assignment expects before you compare answers.
Example: Decimal mode → 127 ÷ 5 = 25.4
Same inputs with Decimal result and default 6 places. After integer pass 25 R 2, the tool brings down 0 → 20; 5 × 4 = 20 exactly. Quotient line reads 25.400000. Decimal bring-down steps are labeled (decimal) in Show your work.
Long division calculator: step-by-step with remainder or decimal
Integer long division with DMSB steps, remainder or decimal output, and answer checks. Non-negative inputs; divisor must be greater than zero. Runs locally.
What this calculator does
The widget divides non-negative integers using the standard long-division algorithm. Enter Dividend (n) and Divisor (d), then pick Quotient with remainder or Decimal result (decimal places 1–20). The dark panel prints quotient and optional remainder; Show your work annotates each DMSB cycle. Divisor must be > 0.
- Division algorithm:
How the math works
Work left to right through dividend digits. When the running partial dividend is at least the divisor, record a quotient digit, subtract the product, and bring down the next digit. In remainder mode, stop when digits are exhausted; the last difference is r. In decimal mode, place a decimal in the quotient and keep bringing down zeros until you hit your place limit.
Secondary example (not the form default): 100 ÷ 7 = 14 R 2. 7 into 10 once (1 × 7 = 7, remainder 3); bring down 0 → 30; 7 into 30 four times (4 × 7 = 28, remainder 2). Check: 7 × 14 + 2 = 100. Repeating decimals (e.g. 1 ÷ 3) truncate at the decimal places you set.
Limits
Only non-negative integer dividend and positive integer divisor (minus signs and other non-digits are stripped from the text fields). JavaScript safe integer range applies. Show your work stops after 100 cycles. Repeating decimals truncate at your place limit. Does not handle fractions or polynomial long division.
Long Division Calculator FAQ
What does the default example return?
Dividend 127, divisor 5, Quotient with remainder → quotient 25, remainder 2. Switch to Decimal result with default 6 decimal places → quotient line 25.400000 (exact value 25.4). Show your work lists each divide/multiply/subtract/bring-down cycle.
What is the difference between remainder and decimal modes?
Quotient with remainder stops when dividend digits are used; the last difference is the remainder (always less than the divisor). Decimal result adds a decimal point in the quotient and keeps bringing down zeros until the decimal-places field (1–20) is filled.
How do you check a long division answer?
Remainder mode: verify . Example: 5 × 25 + 2 = 127. Decimal mode: multiply divisor × decimal quotient; 5 × 25.4 = 127. The dark result panel prints the division sentence under the quotient.
What are the long division steps (DMSB)?
Repeat: Divide (how many times the divisor fits the current partial dividend), Multiply (quotient digit × divisor), Subtract, Bring down the next digit. Show your work annotates each cycle (e.g. "5 goes into 12 2 times; 2 × 5 = 10"). Curricula often call this DMSB inside the bus-stop bracket.
What are dividend, divisor, quotient, and remainder?
The dividend is the number being split; the divisor is how many equal groups you form. The quotient counts whole groups; the remainder is what is left. On the form they are labeled Dividend (n) and Divisor (d).
Why does the widget show a divisor error?
Divisor must be greater than zero. Dividend and divisor are non-negative integers parsed from the text fields. Divisor 0 shows an amber alert instead of a numeric result.
Can this divide fractions or negative numbers?
No. Inputs are non-negative integers only. For fraction arithmetic use the fraction calculator; for quick division without steps use the basic calculator.
How many steps does Show your work print?
One card per DMSB cycle until remainder mode finishes or decimal mode reaches your decimal place limit. The widget caps total cycles at 100 to avoid runaway loops on repeating decimals like 1 ÷ 3.
Mathematical Reference Note
Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.
Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.
Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.
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