Use this calculator to perform integer division and see the step-by-step process of long division. Enter the dividend (the number being divided) and the divisor (the number dividing).
Result:
Steps:
Understanding Division and Long Division
Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is the process of splitting a number into equal parts or groups. When you divide, you're essentially asking, "How many times does one number fit into another?"
Key Terms in Division:
Dividend: The number being divided. It's the total amount you're starting with.
Divisor: The number by which the dividend is divided. It's the size of each group or the number of groups you want to create.
Quotient: The result of the division. It tells you how many whole times the divisor fits into the dividend.
Remainder: The amount left over after the division, when the dividend cannot be perfectly divided by the divisor. The remainder is always less than the divisor.
The relationship between these terms can be expressed as: Dividend = Quotient × Divisor + Remainder.
What is Long Division?
Long division is a standard algorithm used to divide large numbers, breaking down the division problem into a series of simpler steps. It's particularly useful when the dividend is a multi-digit number and the division cannot be easily done mentally. The process involves repeatedly dividing, multiplying, subtracting, and bringing down digits.
How Long Division Works (Step-by-Step Process):
Divide: Look at the first digit (or first few digits) of the dividend. Determine how many times the divisor can go into this partial dividend without exceeding it. This gives you the first digit of your quotient.
Multiply: Multiply the quotient digit you just found by the divisor.
Subtract: Subtract the product from the partial dividend.
Bring Down: Bring down the next digit from the original dividend to form a new partial dividend.
Repeat: Continue these steps (divide, multiply, subtract, bring down) until there are no more digits to bring down. The final number left after the last subtraction is the remainder.
How to Use the Calculator:
Enter Dividend: Input the number you want to divide into the "Dividend" field.
Enter Divisor: Input the number you want to divide by into the "Divisor" field.
Click "Calculate Division": The calculator will instantly display the quotient, the remainder, and a detailed breakdown of each step involved in the long division process.
Examples:
Example 1: Simple Division (1234 ÷ 5)
Let's divide 1234 by 5:
Dividend: 1234
Divisor: 5
Steps:
Bring down 1. Current partial dividend: 1. (1 is less than 5, so we consider more digits)
Bring down 2. Current partial dividend: 12. Divide 12 by 5. Quotient digit: 2. (2 × 5 = 10). Subtract 10 from 12 = 2.
Bring down 3. Current partial dividend: 23. Divide 23 by 5. Quotient digit: 4. (4 × 5 = 20). Subtract 20 from 23 = 3.
Bring down 4. Current partial dividend: 34. Divide 34 by 5. Quotient digit: 6. (6 × 5 = 30). Subtract 30 from 34 = 4.
Result: Quotient = 246, Remainder = 4
Example 2: Division with Zero in Quotient (1005 ÷ 5)
Let's divide 1005 by 5:
Dividend: 1005
Divisor: 5
Steps:
Bring down 1. Current partial dividend: 1. (1 is less than 5, so we consider more digits)
Bring down 0. Current partial dividend: 10. Divide 10 by 5. Quotient digit: 2. (2 × 5 = 10). Subtract 10 from 10 = 0.
Bring down 0. Current partial dividend: 0. (0 is less than 5). Write 0 in the quotient.
Bring down 5. Current partial dividend: 5. Divide 5 by 5. Quotient digit: 1. (1 × 5 = 5). Subtract 5 from 5 = 0.
Result: Quotient = 201, Remainder = 0
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 25px;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
max-width: 800px;
margin: 20px auto;
color: #333;
}
.calculator-container h2 {
color: #2c3e50;
text-align: center;
margin-bottom: 20px;
font-size: 1.8em;
}
.calculator-container h3 {
color: #34495e;
margin-top: 25px;
margin-bottom: 15px;
font-size: 1.4em;
}
.calculator-form label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #555;
}
.calculator-form input[type="number"] {
width: calc(100% – 22px);
padding: 12px;
margin-bottom: 15px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
}
.calculator-form button {
background-color: #007bff;
color: white;
padding: 12px 25px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1.1em;
display: block;
width: 100%;
transition: background-color 0.3s ease;
}
.calculator-form button:hover {
background-color: #0056b3;
}
.calculator-result, .calculator-steps {
background-color: #e9ecef;
padding: 15px;
border-radius: 8px;
margin-top: 20px;
border: 1px solid #dee2e6;
}
.calculator-result p {
font-size: 1.2em;
font-weight: bold;
color: #28a745;
margin: 5px 0;
}
.calculator-steps p {
margin-bottom: 8px;
line-height: 1.6;
color: #495057;
}
.calculator-steps p strong {
color: #007bff;
}
.calculator-article {
margin-top: 30px;
padding-top: 20px;
border-top: 1px solid #eee;
}
.calculator-article p {
line-height: 1.7;
margin-bottom: 15px;
color: #495057;
}
.calculator-article ul, .calculator-article ol {
margin-bottom: 15px;
padding-left: 25px;
color: #495057;
}
.calculator-article ul li, .calculator-article ol li {
margin-bottom: 8px;
}
.calculator-article strong {
color: #34495e;
}
function calculateDivision() {
var dividendInput = document.getElementById("dividend").value;
var divisorInput = document.getElementById("divisor").value;
var dividend = parseInt(dividendInput);
var divisor = parseInt(divisorInput);
var resultDiv = document.getElementById("result");
var stepsDiv = document.getElementById("steps");
resultDiv.innerHTML = "";
stepsDiv.innerHTML = "";
if (isNaN(dividend) || isNaN(divisor)) {
resultDiv.innerHTML = "Please enter valid numbers for both dividend and divisor.";
return;
}
if (divisor === 0) {
resultDiv.innerHTML = "Divisor cannot be zero.";
return;
}
if (dividend === 0) {
resultDiv.innerHTML = "Quotient: 0Remainder: 0″;
stepsDiv.innerHTML = "0 divided by any non-zero number is 0 with a remainder of 0.";
return;
}
var isNegativeResult = (dividend 0) || (dividend > 0 && divisor < 0);
var absDividend = Math.abs(dividend);
var absDivisor = Math.abs(divisor);
if (absDividend < absDivisor) {
resultDiv.innerHTML = "Quotient: " + (isNegativeResult ? "-" : "") + "0Remainder: " + dividend + "";
stepsDiv.innerHTML = "" + absDividend + " is less than " + absDivisor + ", so the quotient is 0 and the remainder is " + dividend + ".";
return;
}
var currentPartialDividend = "";
var currentQuotientDigits = "";
var dividendStr = absDividend.toString();
var steps = [];
var stepCounter = 0;
steps.push("
Long Division Steps for " + absDividend + " ÷ " + absDivisor + ":
");
for (var i = 0; i < dividendStr.length; i++) {
stepCounter++;
currentPartialDividend += dividendStr[i];
var currentNum = parseInt(currentPartialDividend);
steps.push("Step " + stepCounter + ":");
steps.push("Bring down digit " + dividendStr[i] + ". Current partial dividend: " + currentNum + ".");
if (currentNum 0) {
currentQuotientDigits += "0";
steps.push("" + currentNum + " is less than " + absDivisor + ". Write 0 in the quotient.");
}
// If currentQuotientDigits is empty, it means we are at the beginning
// and the first few digits are smaller than the divisor. We don't add '0' yet.
// Example: 1234 / 5. First, 1 < 5. We don't add 0 to quotient. We bring down 2.
// currentPartialDividend becomes "12".
continue;
}
var digitQuotient = Math.floor(currentNum / absDivisor);
var product = digitQuotient * absDivisor;
var stepRemainder = currentNum – product;
currentQuotientDigits += digitQuotient.toString();
steps.push("Divide " + currentNum + " by " + absDivisor + ". The largest multiple of " + absDivisor + " less than or equal to " + currentNum + " is " + product + " (" + digitQuotient + " × " + absDivisor + ").");
steps.push("Write " + digitQuotient + " in the quotient.");
steps.push("Subtract " + product + " from " + currentNum + " = " + stepRemainder + ".");
currentPartialDividend = stepRemainder.toString();
}
var finalQuotient = parseInt(currentQuotientDigits);
var finalRemainder = parseInt(currentPartialDividend);
if (isNegativeResult) {
finalQuotient = -finalQuotient;
}
// Remainder sign convention: remainder has the same sign as the dividend (or is zero).
if (dividend < 0 && finalRemainder !== 0) {
finalRemainder = -finalRemainder;
}
resultDiv.innerHTML = "Quotient: " + finalQuotient + "Remainder: " + finalRemainder + "";
stepsDiv.innerHTML = steps.join("");
}