ganak.appLong Division Calculator
Free long division calculator showing complete step-by-step work. Enter any dividend and divisor to see quotient, remainder, decimal form with repeating detection, and a detailed visual solution process.
The number being divided
The number to divide by
Division Summary
Complete results for 7,425 ÷ 32
Step-by-Step Solution
Long division of 7,425 by 32 shown in full
23232 )─────742564──10296───6564──1
32 goes into 74 → 2 times (32 × 2 = 64). Subtract: 74 − 64 = 10. Bring down 2 to get 102.
32 goes into 102 → 3 times (32 × 3 = 96). Subtract: 102 − 96 = 6. Bring down 5 to get 65.
32 goes into 65 → 2 times (32 × 2 = 64). Subtract: 65 − 64 = 1. No more digits. Remainder is 1.
Related Information
All representations of this division
What Is Long Division?
Understanding the parts and purpose of long division
Long division is a standard method for dividing large numbers that cannot be easily divided mentally. It breaks a complex division problem into a series of simpler steps, writing out each intermediate calculation so the work is easy to follow and verify.
Division Formula
Dividend ÷ Divisor = Quotient remainder Remainder
Dividend
The number being divided
Divisor
The number you divide by
Quotient
The result of the division
Remainder
The amount left over
How to Do Long Division Step-by-Step
The 5-step algorithm: Divide, Multiply, Subtract, Bring Down, Repeat
Divide
Determine how many times the divisor fits into the current working number. Write that digit above the division bar.
Multiply
Multiply the divisor by the quotient digit. Write the product below the working number, aligned to the right.
Subtract
Subtract the product from the working number. Write the difference below, aligned to the right.
Bring Down
Bring down the next unused digit from the dividend and append it to the remainder. This forms the new working number.
Repeat
Repeat steps 1–4 until all digits have been brought down. The leftover is the remainder. If you need a decimal answer, add a decimal point and zeros, then continue.
Long Division with Decimals
Continuing past the remainder for an exact or repeating decimal
When you reach the end of the dividend's digits and still have a remainder, you can continue dividing by placing a decimal point in the quotient and appending zeros to the remainder. Each new zero lets you perform another round of divide-multiply-subtract.
Terminating Decimals
Some divisions end exactly. For example, 7 ÷ 4 = 1.75. This happens when the divisor's prime factors are only 2 and/or 5. The remainder eventually becomes zero.
Repeating Decimals
Some divisions never end. For example, 1 ÷ 3 = 0.333... The same digits repeat forever. This happens when the remainder enters a cycle. You can identify the pattern when you see a remainder you've encountered before.
Real-World Applications
Where long division is used in everyday life
Splitting Bills
Divide a restaurant bill of $247 among 6 people: 247 ÷ 6 = $41.16 each with $0.04 remaining.
Converting Units
Convert 5280 feet to miles: 5280 ÷ 5280 = 1 mile. Or 10,000 meters to kilometers: 10,000 ÷ 1000 = 10 km.
Distributing Items
Distribute 150 candies equally among 7 children: 150 ÷ 7 = 21 each with 3 left over.
Scaling Recipes
A recipe for 12 servings needs 750g flour. For 5 servings: 750 ÷ 12 × 5 = 312.5g flour.
Common Mistakes in Long Division
Errors to watch out for when dividing by hand
Forgetting to Bring Down
After subtracting, always bring down the next digit before dividing again. Skipping this step produces a quotient with missing digits.
Skipping Zeros in the Quotient
When the working number is smaller than the divisor after bringing down, you must place a zero in the quotient. Forgetting this shifts all subsequent digits left, giving a wrong answer. For example, 3204 ÷ 32 = 100 R 4, not 14.
Misplacing the Decimal Point
When continuing division into decimals, the decimal point in the quotient must align directly above the decimal point in the dividend. Misalignment makes the answer 10x too large or too small.
Not Checking Your Work
Always verify by multiplying: quotient × divisor + remainder should equal the dividend. This quick check catches most arithmetic errors.
Frequently Asked Questions
Common questions about long division, remainders, and decimals