Long Division Calculator
Solve long division problems step by step. See each divide → multiply → subtract iteration, the quotient, remainder, decimal result, and full step-by-step working.
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How It Works
Look at the leftmost digit(s) of the dividend. Find the largest multiple of the divisor that fits into this number. Write that multiple's factor above the dividend.
How many times does 32 go into 48?48 ÷ 32 = 1 (write 1 above)Multiply the divisor by the quotient digit you just wrote. Write this product below the portion of the dividend you are working with.
divisor × quotient digit32 × 1 = 32 (write below 48)Subtract the product from the digits above it. Write the result below. This becomes the carry-forward for the next step.
current number − product48 − 32 = 16Bring down the next digit from the dividend and append it to the current remainder. This forms the new number to divide in the next iteration.
append next digit16 → 167 (bring down 7)After all dividend digits are used, if a remainder exists, add a decimal point to the quotient and a zero to the remainder. Continue dividing until desired precision.
remainder × 10 then divide7 ÷ 32 = 0.21875Always verify: divisor × quotient + remainder = dividend. For decimal results: quotient × divisor ≈ dividend (within rounding).
divisor × quotient + remainder = dividend32 × 15 + 7 = 487 ✓Quick Reference
Common examples — verify instantly above.
Exact
144 ÷ 12
12 R 0 = 12
Remainder
487 ÷ 32
15 R 7
Decimal
10 ÷ 3
3 R 1 = 3.333...
Simple
75 ÷ 4
18 R 3 = 18.75
Large
1234 ÷ 56
22 R 2
Small div
7 ÷ 2
3 R 1 = 3.5
Large div
9999 ÷ 99
101 R 0
Decimal
22 ÷ 7
3 R 1 ≈ 3.1429
Tips & Shortcuts
At each step, the number you bring down must be at least as large as the divisor before you can write a non-zero quotient digit. If not, write 0 and bring down another digit.
Double-check by multiplying back: divisor × quotient + remainder must equal dividend. This takes 10 seconds and catches most errors.
When the partial dividend is smaller than the divisor, write 0 in the quotient and bring down the next digit before dividing.
For repeating decimals, look for a remainder that has appeared before — when you see it again, the decimal pattern repeats from that point.
If you make an error in the multiply step, every subsequent step will be wrong. Always verify the multiply before subtracting.
Estimation helps: round the divisor to a nice number first. 487 ÷ 32 ≈ 487 ÷ 30 ≈ 16. This tells you the quotient should be around 15-16.
Common Mistakes
Forgetting to write a 0 in the quotient when the partial dividend is smaller than divisor
If the divisor does not fit into the current partial dividend, write 0 in the quotient position and bring down the next digit before dividing.
Subtracting the dividend from the product instead of product from dividend
Always compute: partial dividend − (quotient digit × divisor). The result should be smaller than the divisor.
Not bringing down a digit before continuing
After each subtraction, you must bring down the next digit. The number of quotient digits equals the number of dividend digits (or more for decimals).
Stopping when remainder is less than divisor instead of zero
You stop when there are no more digits to bring down, not just when remainder < divisor. If remainder > 0 and you want a decimal, continue with zeros.
Misplacing the quotient digit above the wrong column
Each quotient digit goes directly above the last digit of the group you divided. Alignment errors cause the entire quotient to be wrong.
Forgetting to verify the answer
Always check: divisor × quotient + remainder = dividend. A 10-second check prevents submitting or using a wrong answer.
Frequently Asked Questions
Long division is an algorithm for dividing large numbers step by step: divide, multiply, subtract, and bring down the next digit. Repeat until all digits are used.
Four repeating steps: 1) Divide: how many times does divisor fit? 2) Multiply: divisor × quotient digit. 3) Subtract: from current number. 4) Bring down: next digit from dividend.
The remainder is what is left over after the last subtraction step. If the remainder is 0, the division is exact.
Once you run out of dividend digits, add a decimal point to the quotient and bring down zeros, continuing the process to as many decimal places as needed.
Long division teaches the structure of the number system and builds mental arithmetic skills. It is also required in algebra for polynomial division.
Use: divisor × quotient + remainder = dividend. Example: if 487 ÷ 32 = 15 R 7, check: 32 × 15 + 7 = 480 + 7 = 487 ✓
The remainder is what is left after dividing as many whole times as possible. For 17 ÷ 5: 5 goes into 17 three times (5×3=15), remainder = 17−15 = 2. Written as: 17 = 5×3 + 2, or as a fraction 17/5 = 3⅖, or as decimal 3.4. The remainder is always smaller than the divisor — if it equals or exceeds the divisor, you can divide one more time.
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