The formula this page uses
dividend ÷ divisor = quotient with remainder r, and the check is divisor × quotient + r = dividend
Work through long division one digit at a time
Use the free long division calculator to work through the number relationship, preserve exact values, and check the result with estimation.
MGT
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Arithmetic
Long Division Calculator explained
The short version
- Long division works one digit at a time: divide, multiply, subtract, bring the next digit down.
- Keep the digits in straight columns, because a digit written in the wrong column changes the answer by a factor of ten.
- When you run out of digits you can either stop with a remainder or add a decimal point and keep going.
What each part means
SymbolWhat it means
dividend — The number being sharedThe one that goes inside the division bracket.
divisor — The number you are dividing byThe one outside. It must not be 0.
quotient — The answer on topOne digit appears for each digit you bring down.
r — The remainderWhat is left at the end. It is always smaller than the divisor.
Show your work: a full example
- Divide 4728 by 124728 ÷ 12
- 12 does not fit into 4, so look at 4712 fits into 47 three times, because 3 × 12 = 36 and 4 × 12 = 48 is too big
- Subtract and bring down the 247 − 36 = 11, then bring down the 2 to make 112
- Divide again12 fits into 112 nine times, because 9 × 12 = 108 and 10 × 12 = 120 is too big
- Subtract and bring down the 8112 − 108 = 4, then bring down the 8 to make 48
- Divide the last one48 ÷ 12 = 4 exactly, remainder 0
- Read the answer off the top4728 ÷ 12 = 394
- Check12 × 394 = 4728
A second, different case
- A different case: the remainder becomes a decimal725 ÷ 8
- 8 does not fit into 7, so look at 7272 ÷ 8 = 9 exactly, remainder 0
- Bring down the 55 ÷ 8 = 0, remainder 5, so far the answer is 90 remainder 5
- Add a decimal point and a zero50 ÷ 8 = 6, and 6 × 8 = 48, remainder 2
- Add another zero20 ÷ 8 = 2, and 2 × 8 = 16, remainder 4
- And another40 ÷ 8 = 5, and 5 × 8 = 40, remainder 0
- Put it together725 ÷ 8 = 90.625
Copy-ready example
4728 ÷ 12
Divide 4728 by 12
Questions about the Long Division Calculator
What do I do when the divisor is bigger than the first digits?
Write a 0 in that spot and take one more digit. Dividing 725 by 8 starts with 7 ÷ 8 = 0, so you move straight on to 72. Writing that 0 matters when it sits in the middle of an answer, because skipping it is what turns 405 into 45.
Should my answer be a remainder or a decimal?
It depends on what is being shared. Buses and boxes need whole answers, so 725 people in groups of 8 gives 90 full groups with 5 left over. Money and measurements want the decimal, so 725 grams shared 8 ways is 90.625 grams each.
How can I check a long division quickly?
Multiply the answer back by the divisor and add any remainder. Here 12 × 394 = 4728, which matches, so the division is right. This check catches almost every column error and takes ten seconds.
Any tips for dividing by a two-digit number?
Round the divisor to guess each digit. When dividing by 12 you can think of it as 'about 10' to guess, then correct: for 112 a first guess of 11 is too big since 11 × 12 = 132, so try 9, and 9 × 12 = 108 fits. Guessing and correcting is faster than working it out exactly each time.
How to use the Long Division Calculator
Use the interactive workspace first, then connect the output to the mathematical definitions and checks below.
What the four-function calculator handles
Use standard arithmetic, parentheses, sign changes, percentages, memory registers, answer recall, and an editable calculation tape. The separate percentage workspace covers percent-of, percent-change, increases, discounts, tax, tips, and split totals.
Order of operations and percentages
Parentheses are evaluated first, followed by multiplication or division and then addition or subtraction at equal priority from left to right. A percent is a ratio per hundred; always identify the base quantity before calculating a discount or change.
How to verify everyday calculations
Estimate before entering values, keep money rounding until the final total, and use an inverse operation when possible. For a split bill, verify that the per-person amount multiplied by the group size returns the calculated total.
Need a complete explanation?
Send the exact question and your current work to MathGPT for a step-by-step method and an independent check.
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Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.