Free Long Division Calculator - Step-by-Step Work Shown

Our free Long Division Calculator performs division with complete visual step-by-step work. See every divide, multiply, subtract, and bring down operation. Detects repeating decimals and shows results in multiple forms.

What is Long Division?

Long division is a standard mathematical algorithm for dividing large numbers by breaking the problem into a series of simpler steps. Unlike mental math or short division, long division writes out every step, making it easy to follow and verify.

The method works by repeatedly dividing, multiplying, subtracting, and bringing down digits from the dividend until you reach a remainder of zero or the desired number of decimal places.

Parts of Long Division

• Dividend — The number being divided (the large number)
• Divisor — The number you are dividing by
• Quotient — The result (answer)
• Remainder — What is left over after division

How to Do Long Division Step by Step

Long division follows five repeating steps:

Step 1: Divide

Take the first digit (or digits) of the dividend that are large enough to be divided by the divisor. Calculate how many times the divisor goes into those digits.

Step 2: Multiply

Multiply the divisor by the quotient digit you just found. Write the product under the digits you divided into.

Step 3: Subtract

Subtract the product from the digits above it. The difference must be less than the divisor.

Step 4: Bring Down

Bring down the next digit from the dividend and append it to the remainder from the subtraction.

Step 5: Repeat

Repeat steps 1–4 until all digits have been processed. If there is a remainder and you want decimal places, add a decimal point and zeros, then continue.

How to Use This Calculator

1. Enter the dividend (number to divide)
2. Enter the divisor (number to divide by)
3. Select the number of decimal places (2, 4, 6, 10, or 20)
4. View the complete step-by-step work

Example: 144 ÷ 12

  12
  ---
12|144
  12
  --
   24
   24
   --
    0

Result: 144 ÷ 12 = 12 with remainder 0

Example: 22 ÷ 7

   3.142857...
   ---------
7|22.000000
  21
  --
   10
    7
   ---
   30
   28
   --
    20
    14
   ---
     60
     56
    ---
      40
      35
     ---
       50
       49
      ---
        1

Result: 22 ÷ 7 = 3.142857... (repeating)

Features

• Visual division bracket — See the work laid out like paper
• Step-by-step breakdown — Every divide, multiply, subtract, bring down
• Adjustable precision — Choose 2 to 20 decimal places
• Repeating decimal detection — Automatically detects and labels repeating patterns
• Multiple result forms — Quotient, remainder, decimal, and fraction
• Quick examples — Load common problems with one click
• Works with large numbers — No size limitations

Long Division with Decimals

When the divisor doesn't go evenly into the dividend, you get a remainder. To continue dividing into decimals:

1. Place a decimal point after the quotient
2. Add zeros to the right of the dividend
3. Bring down zeros and continue the division process
4. Continue until the remainder is zero or you reach desired precision

When Do Decimals Repeat?

Some divisions produce repeating decimals. This happens when the remainder starts cycling through values you have already seen. For example:

1 ÷ 3 = 0.333... (repeating 3)

1 ÷ 7 = 0.142857142857... (repeating block of 6 digits)

Long Division with Remainders

When a number doesn't divide evenly, the result can be expressed as:

• Decimal form: 17 ÷ 5 = 3.4
• Remainder form: 17 ÷ 5 = 3 R 2
• Mixed number: 17 ÷ 5 = 3 2/5
• Fraction form: 17 ÷ 5 = 17/5

Long Division Tips and Tricks

• Estimate first — Round numbers to check if your answer is reasonable
• Check your work — Multiply quotient × divisor + remainder = dividend
• Watch your alignment — Keep digits properly aligned in columns
• Practice with easier numbers — Start with single-digit divisors before moving to two-digit
• Use multiplication facts — Knowing your times tables speeds up the divide step

Real-World Applications

Splitting Costs

Dividing a restaurant bill of $127 among 6 people: 127 ÷ 6 = $21.16 per person (with $0.04 remainder).

Measurements

Cutting a 96-inch board into 7 equal pieces: 96 ÷ 7 = 13.71 inches each.

Cooking

Scaling a recipe that serves 4 to serve 15: multiply all ingredients by 15 ÷ 4 = 3.75.

Finance

Calculating monthly payments on a $5,000 purchase over 18 months: 5000 ÷ 18 = $277.78/month.

Travel

Dividing a 483-mile trip into 3 driving days: 483 ÷ 3 = 161 miles per day.

FAQs About Long Division Calculator

How do you do long division step by step?

Write the divisor outside the bracket and the dividend inside. Divide the first digits, write the quotient on top, multiply it by the divisor, subtract, bring down the next digit, and repeat until complete.

How to do long division with 2-digit divisors?

The process is the same. You estimate how many times the two-digit divisor goes into the first few digits of the dividend. For example, with divisor 25 and dividend 175, test: 25 × 7 = 175, so the quotient is 7.

How to do long division with decimals?

Add a decimal point to the quotient directly above the dividend's decimal point. Then bring down zeros and continue dividing. Keep going until the remainder is zero or you have enough decimal places.

What is a remainder in long division?

A remainder is what is left after division when the divisor doesn't go into the dividend evenly. For example, 17 ÷ 5 = 3 remainder 2, because 5 × 3 = 15, and 17 − 15 = 2.

How to check your long division answer?

Multiply the quotient by the divisor and add the remainder. The result should equal the original dividend: quotient × divisor + remainder = dividend.

What are repeating decimals?

Repeating decimals occur when the division process never reaches a remainder of zero. The same sequence of digits repeats forever. For example, 1 ÷ 3 = 0.333... where 3 repeats infinitely.

What is the difference between short division and long division?

Short division is a faster method where most calculations are done mentally. Long division writes out every step, making it better for larger numbers or when learning the concept.

Can long division handle negative numbers?

Yes. Divide the absolute values normally, then apply the sign rule: positive ÷ positive = positive, negative ÷ positive = negative, positive ÷ negative = negative, and negative ÷ negative = positive.

How do you express a remainder as a fraction?

Place the remainder over the divisor. For example, 17 ÷ 5 = 3 with remainder 2, which equals 3 2/5 or 17/5 as an improper fraction.

Why is long division important?

Long division builds number sense, reinforces multiplication and subtraction skills, and provides a foundation for understanding more advanced math concepts like polynomial division and algorithms in computer science.

Why Use Our Long Division Calculator?

• Free and instant — No registration, no downloads
• Visual work shown — See every step like on paper
• Repeating decimal detection — Automatically identifies patterns
• Adjustable precision — Choose your decimal places
• Educational — Learn by following the steps
• Privacy focused — All calculations run in your browser
• Mobile friendly — Works on any device

Master long division with our free step-by-step calculator!