Long division calculator
This long division calculator shows every step: enter the dividend and divisor and get the quotient, the remainder, each working step and the check. 4536 ÷ 12 is 378; 1234 ÷ 5 is 246 remainder 4, or 246.8 with decimals. Long multiplication is included too.
Example: What do you want to work out: Long division · First number (dividend or factor) 4,536 · Second number (divisor or factor) 12 · Decimal places in the result 0 → Result: 4536 : 12 = 378. Source: Wikipedia – Long division. Updated: .
How it is calculated
How long division works
You divide the dividend digit by digit. First take as many digits from the left as are needed for the number to be at least as large as the divisor. Then, for each step: quotient digit = number ÷ divisor (rounded down), product = digit × divisor, remainder = number − product. Bring down the next digit next to the remainder and repeat.
- 4536 ÷ 12: 45 ÷ 12 = 3 (remainder 9), 93 ÷ 12 = 7 (remainder 9), 96 ÷ 12 = 8 (remainder 0) → 378
- 1234 ÷ 5 = 246 remainder 4
- With decimals: 4 is left over, so 40 ÷ 5 = 8 → 1234 ÷ 5 = 246.8
Decimal places
If a remainder is left at the end, put a decimal point in the result and add a zero to the remainder. The calculator does this for the number of places you choose. The digits are truncated, not rounded – for 1 ÷ 3, four places give 0.3333.
The check
Quotient × divisor + remainder = dividend. For 1234 ÷ 5: 246 × 5 + 4 = 1234. The check shows whether you made a slip.
Long multiplication
Multiply the first number by each digit of the second, starting with the ones, and write the partial products shifted one place each (that is times 10, times 100 …). The sum of the partial products is the answer: 4536 × 12 = 9072 + 45360 = 54432.
Honest limits
How the working is laid out (bars, alignment, notation) differs between schools and countries; the calculator shows the steps as text. It works with whole numbers of up to 15 digits; decimals as dividend or divisor are not supported.
Frequently asked questions
How does long division work?
Divide digit by digit: number by divisor, form the product, work out the remainder and bring down the next digit. 4536 ÷ 12 gives 378 this way.
How do I do long division with decimals?
If a remainder is left, put a decimal point in the result and add a zero to the remainder. 1234 ÷ 5 = 246 remainder 4, so 246.8.
How do I check a division?
Quotient times divisor plus remainder must give the dividend: 246 × 5 + 4 = 1234.
What if the divisor is larger than the first digits?
Take one more digit until the number is at least as large as the divisor.
How does long multiplication work?
Multiply the first number by each digit of the second, write the partial products shifted by place and add them: 4536 × 12 = 9072 + 45360 = 54432.
Sources and legal basis
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