Long Division Step-by-Step Calculator
Divide any whole numbers and see the manual calculation process.
Understanding Long Division
Long division is a standard algorithm used to divide multi-digit numbers. It breaks down a complex division problem into a series of simpler steps involving division, multiplication, subtraction, and "bringing down" the next digit of the dividend.
Dividend ÷ Divisor = Quotient (with a Remainder)
Key Terms to Remember
- Dividend: The total amount you have that you want to divide up.
- Divisor: The number you are dividing by.
- Quotient: The answer (how many times the divisor fits into the dividend).
- Remainder: The amount left over that is smaller than the divisor.
The 4-Step Process: DMSB
Most students learn the acronym DMSB to remember the order of operations in long division:
| Step | Action | Description |
|---|---|---|
| D | Divide | See how many times the divisor goes into the current working number. |
| M | Multiply | Multiply the divisor by your new quotient digit. |
| S | Subtract | Subtract that result from your working number to find the difference. |
| B | Bring Down | Bring down the next digit from the dividend to create a new working number. |
Example: 484 ÷ 4
1. Divide: 4 goes into 4 (the first digit) 1 time. Quotient starts with 1.
2. Multiply & Subtract: 4 x 1 = 4. 4 – 4 = 0.
3. Bring Down: Bring down the 8. New number is 08.
4. Repeat: 4 goes into 8 exactly 2 times. 8 – 8 = 0.
5. Bring Down: Bring down the 4. 4 goes into 4 exactly 1 time.
6. Final Answer: 121.
Frequently Asked Questions
What if the divisor is larger than the dividend?
If the divisor is larger, the quotient will be 0 and the entire dividend becomes the remainder (or you move into decimals).
How do I check my answer?
Multiply the Quotient by the Divisor and add the Remainder. The result should equal the Dividend: (Quotient × Divisor) + Remainder = Dividend.
";
stepsHtml += "Step " + (i + 1) + ":";
stepsHtml += "Current working number: " + workingValue + "";
stepsHtml += "How many times does " + divisor + " go into " + workingValue + "? " + tempQuotient + " times.";
stepsHtml += "Multiply: " + tempQuotient + " × " + divisor + " = " + product + "";
stepsHtml += "Subtract: " + workingValue + " – " + product + " = " + newRemainder + "";
if (i < dividendStr.length – 1) {
stepsHtml += "Bring down " + dividendStr[i+1] + " to make " + ((newRemainder * 10) + parseInt(dividendStr[i+1]));
} else {
stepsHtml += "No more digits to bring down.";
}
stepsHtml += "
";
quotientStr += tempQuotient.toString();
currentRemainder = newRemainder;
}
// Clean up leading zeros in quotient unless quotient is just "0"
var finalQuotient = parseInt(quotientStr);
finalAnswer.innerHTML = "Result: " + dividend + " ÷ " + divisor + " = " + finalQuotient + " R " + currentRemainder + "";
stepContainer.innerHTML = stepsHtml;
}