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Long Division Calculator

Step-by-step long division calculator.

Dividend & divisor

Enter the dividend (number being divided) and the divisor (number that divides). Choose quotient with remainder or a decimal result.

The number being divided.

The number that divides the dividend.

Result
Quotient25
Remainder2

127 รท 5 = 25 R 2

Show your work

Standard long division (divide, multiply, subtract, bring down).

Dividend รท Divisor
127 รท 5
= 25 R 2

5 goes into 12 2 times; 2 ร— 5 = 10

12 โˆ’ 10 = 2 โ†’ bring down 7

5 goes into 27 5 times; 5 ร— 5 = 25

27 โˆ’ 25 = 2

Using the Long Division Calculator

Use the calculator above: enter the dividend and divisor, then choose quotient with remainder or a decimal result (and decimal places). The article below explains the parts of division and how to perform long division manually.

Workflow Tips

Dividend & divisor

Enter dividend and divisor (both non-negative; divisor > 0). The article below defines these terms.

Quotient with remainder

Select "Quotient with remainder" for whole-number quotient and remainder; the article below explains remainders.

Decimal result

Select "Decimal result" and set decimal places to get a decimal quotient; the tool brings down zeros and shows each step.

Show your work

Each step is annotated; the article below explains the divide, multiply, subtract, and bring down steps.

Long Division Calculator: Step-by-Step with Remainder or Decimal

Free long division calculator: quotient with remainder or decimal result. How to do long division with remainders, long division steps for kids, division with decimals. Dividend divisor quotient remainder explained.

What This Calculator Does & Who It's For

Calculator Purpose & Ideal Users

This long division calculator gives step-by-step long division: it performs division and shows every step of the standard algorithm (divide, multiply, subtract, bring down). You get either a quotient with remainder or a decimal result to a chosen number of decimal places.
  • What You'll Get:
    Quotient and remainder: e.g. 127 รท 5 = 25 R 2. Decimal result: Optional, with configurable decimal places. Show your work: Each step with annotations (e.g. "5 goes into 12 2 times; 2 ร— 5 = 10") and a clear dividend รท divisor summary. Validation: Non-negative integers; divisor must be > 0.
  • Scope & Limits:
    Non-negative integers only. Divisor must be greater than zero. Results and steps within JavaScript safe integer range.

How the Math Works

The Division Algorithm

Every integer division can be expressed by the division algorithm:
a=dร—q+rwhereย 0โ‰คr<da = d \times q + r \quad \text{where } 0 \le r < d

where a is the dividend, d is the divisor, q is the quotient, and r is the remainder. This identity is the foundation of the long division process, each step finds quotient digits that satisfy this relationship.

  • a (Dividend):
    The number being divided
  • d (Divisor):
    The number dividing into the dividend (must be > 0)
  • q (Quotient):
    How many whole times the divisor fits into the dividend
  • r (Remainder):
    What is left over; always satisfies 0 โ‰ค r < d

The Long Division Algorithm (DMSB)

The standard long division procedure processes the dividend digit by digit from left to right using four repeating steps:
Divideโ†’Multiplyโ†’Subtractโ†’Bringย downโŸrepeatย forย eachย digit\underbrace{\text{Divide} \to \text{Multiply} \to \text{Subtract} \to \text{Bring down}}_{\text{repeat for each digit}}

Divide: Determine how many times the divisor fits into the current working number. Multiply: Quotient digit ร— divisor. Subtract: Working number โˆ’ product. Bring down: Append the next digit of the dividend to the difference and repeat.

  • Decimal Extension:
    To convert a remainder to a decimal, add a decimal point to the quotient and "bring down" zeros, continuing the DMSB cycle for each decimal place
  • Termination:
    Whole-number mode stops when all digits are processed; decimal mode stops at the requested number of decimal places

Worked Example

127 รท 5:

  • Step 1 (Divide): 5 goes into 1 zero times โ†’ bring down 2 to make 12
  • Step 2 (Divide): 5 goes into 12 two times โ†’ Multiply: 2 ร— 5 = 10 โ†’ Subtract: 12 โˆ’ 10 = 2 โ†’ bring down 7 to make 27
  • Step 3 (Divide): 5 goes into 27 five times โ†’ Multiply: 5 ร— 5 = 25 โ†’ Subtract: 27 โˆ’ 25 = 2
  • Result: 127 รท 5 = 25 remainder 2

Decimal continuation: Bring down a 0 โ†’ 20 รท 5 = 4 exactly. So 127 รท 5 = 25.4.

Verify: 5 ร— 25 + 2 = 127 โœ“ and 5 ร— 25.4 = 127.0 โœ“

  • Repeating Decimals:
    Some divisions never terminate (e.g., 1 รท 3 = 0.333โ€ฆ). The calculator shows the result to your chosen decimal places
  • Limitation:
    This calculator handles non-negative integers only; divisor must be greater than zero. Results stay within JavaScript safe integer range

How to Use This Calculator

Enter the dividend (the number being divided) and the divisor (the number dividing into it), then choose whether you want a quotient with remainder or a decimal result. For decimal mode, set the number of decimal places you need. The calculator walks through each divide, multiply, subtract, and bring-down step so you can follow the same process you would perform by hand on paper.
  • Dividend:
    The number being divided. Enter a non-negative integer in the Dividend field. This is the starting number that gets broken down by the divisor.
  • Divisor:
    The number that divides into the dividend. Must be greater than zero. The algorithm determines how many times this fits into successive portions of the dividend.
  • Result Type:
    Choose "Quotient with remainder" for a whole-number answer plus leftover, or "Decimal result" to continue dividing by bringing down zeros to the precision you specify.
  • Show Your Work:
    Each step is annotated with what the divisor goes into, how many times, the multiplication, and the subtraction, matching the standard DMSB (Divide, Multiply, Subtract, Bring down) procedure.

Components of Division: Dividend, Divisor, Quotient, Remainder Explained

Dividend, divisor, quotient, and remainder explained: In division, the dividend is the number being divided; the divisor is the number that divides it. The quotient is the result (how many times the divisor fits), and the remainder is what is left over. So dividend รท divisor = quotient with remainder, or dividend = divisor ร— quotient + remainder. For example, 127 รท 5 = 25 R 2 means 127 = 5 ร— 25 + 2. The remainder is always less than the divisor. Every long division calculator uses this breakdown; for "What is the number being divided called?" and "What is a remainder?", see the FAQ above.

How to Perform Long Division Manually

To perform long division (the standard "bus stop" method): (1) Divide, take the leftmost digits of the dividend that are at least the divisor; see how many times the divisor fits (that is your first quotient digit). (2) Multiply, multiply that quotient digit by the divisor. (3) Subtract, subtract that product from the current portion. (4) Bring down, bring down the next digit of the dividend and repeat. When you run out of digits, what is left is the remainder. These are the long division steps for kids and adults alike; many curricula teach them as DMSB (Divide, Multiply, Subtract, Bring down). For a decimal result, add a decimal point and bring down zeros. This long division calculator shows these steps for any dividend and divisor; the "Show your work" section annotates each step (e.g. "7 goes into 30 four times; 4 ร— 7 = 28").

Long Division with Remainders

Long division with remainders stops when you have used all digits of the dividend and the last difference is less than the divisor, that difference is the remainder. For example, 100 รท 7 = 14 R 2. To turn a remainder into a decimal, continue by writing a decimal point and bringing down zeros; the calculator's "Decimal result" mode does this and shows the steps. For "How do you turn a remainder into a decimal?" see the FAQ above.

Division with Decimals

For a division with decimals result, use the same long division algorithm: after processing all digits of the dividend, add a decimal point in the quotient and "bring down" zeros. Each zero gives another decimal place. For example, 1 รท 2: 2 goes into 10 five times (0.5). A division with decimals calculator like this one lets you set the number of decimal places and see every step; select "Decimal result" and choose your precision to get a decimal quotient.

Long Division Calculator FAQ

What is the number being divided called?

The number being divided is called the dividend. The number that divides it is the divisor. The result is the quotient, and any amount left over is the remainder. So in 127 รท 5 = 25 R 2, 127 is the dividend, 5 is the divisor, 25 is the quotient, and 2 is the remainder.

What is a remainder?

The remainder is what is left after dividing the dividend by the divisor as many whole times as possible. So 127 รท 5 = 25 with remainder 2 because 5 ร— 25 = 125 and 127 โˆ’ 125 = 2. The remainder is always less than the divisor. Choose "Quotient with remainder" in the calculator to see the remainder; choose "Decimal result" to continue the division and get a decimal answer.

How do you turn a remainder into a decimal?

To turn a remainder into a decimal, continue the long division by adding a decimal point and "bringing down" zeros. For example, 127 รท 5 = 25 R 2; then 2 with a zero brought down gives 20, 5 goes into 20 four times (0.4), so 127 รท 5 = 25.4. Select "Decimal result" in this calculator and set the number of decimal places to see the steps of adding zeros and getting the decimal answer.

How do you do long division with remainders?

Use the standard long division steps: Divide (how many times the divisor fits into the current portion), Multiply (quotient digit ร— divisor), Subtract, then Bring down the next digit. Repeat until you run out of digits. What is left is the remainder. This calculator shows each step with annotations (e.g. "5 goes into 12 2 times; 2 ร— 5 = 10"). Select "Quotient with remainder" to see the remainder.

What are the long division steps for kids?

The long division steps are often taught as: (1) Divide, see how many times the divisor fits into the first digit(s); (2) Multiply, multiply that number by the divisor; (3) Subtract, take that product away from the current number; (4) Bring down, bring down the next digit and repeat. This is the "bus stop" or bracket method. The calculator's "Show your work" section displays these long division steps for any dividend and divisor.

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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