function displayError(message) {
document.getElementById('integerResult').innerHTML = " + message + ";
}
function getInputs() {
var int1 = parseInt(document.getElementById('integer1').value);
var int2 = parseInt(document.getElementById('integer2').value);
if (isNaN(int1) || isNaN(int2)) {
displayError("Please enter valid integers for both fields.");
return null;
}
return { int1: int1, int2: int2 };
}
function calculateAddition() {
var inputs = getInputs();
if (!inputs) return;
var result = inputs.int1 + inputs.int2;
document.getElementById('integerResult').innerHTML = 'Sum: ' + result + ";
}
function calculateSubtraction() {
var inputs = getInputs();
if (!inputs) return;
var result = inputs.int1 – inputs.int2;
document.getElementById('integerResult').innerHTML = 'Difference: ' + result + ";
}
function calculateMultiplication() {
var inputs = getInputs();
if (!inputs) return;
var result = inputs.int1 * inputs.int2;
document.getElementById('integerResult').innerHTML = 'Product: ' + result + ";
}
function calculateDivision() {
var inputs = getInputs();
if (!inputs) return;
if (inputs.int2 === 0) {
displayError("Cannot divide by zero.");
return;
}
var quotient = Math.floor(inputs.int1 / inputs.int2);
var remainder = inputs.int1 % inputs.int2;
document.getElementById('integerResult').innerHTML = 'Quotient: ' + quotient + 'Remainder: ' + remainder + ";
}
function calculateGCD() {
var inputs = getInputs();
if (!inputs) return;
var a = Math.abs(inputs.int1);
var b = Math.abs(inputs.int2);
// Handle GCD(0, x) = |x| and GCD(x, 0) = |x|
if (a === 0) {
document.getElementById('integerResult').innerHTML = 'GCD: ' + b + ";
return;
}
if (b === 0) {
document.getElementById('integerResult').innerHTML = 'GCD: ' + a + ";
return;
}
while (b) {
var temp = b;
b = a % b;
a = temp;
}
document.getElementById('integerResult').innerHTML = 'GCD: ' + a + ";
}
function calculateLCM() {
var inputs = getInputs();
if (!inputs) return;
var a = inputs.int1;
var b = inputs.int2;
// Handle LCM(0, x) = 0
if (a === 0 || b === 0) {
document.getElementById('integerResult').innerHTML = 'LCM: 0′;
return;
}
// Inlined GCD function for LCM calculation
var gcdVal = (function(num1, num2) {
num1 = Math.abs(num1);
num2 = Math.abs(num2);
while (num2) {
var temp = num2;
num2 = num1 % num2;
num1 = temp;
}
return num1;
})(a, b);
var lcmVal = (Math.abs(a * b)) / gcdVal;
document.getElementById('integerResult').innerHTML = 'LCM: ' + lcmVal + ";
}
.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
font-family: Arial, sans-serif;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
color: #555;
font-weight: bold;
}
.input-group input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.button-group {
display: flex;
flex-wrap: wrap;
gap: 10px;
margin-top: 20px;
justify-content: center;
}
.button-group button {
background-color: #007bff;
color: white;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
flex: 1 1 auto; /* Allow buttons to grow and shrink */
min-width: 120px; /* Minimum width for buttons */
}
.button-group button:hover {
background-color: #0056b3;
}
.result-container {
margin-top: 25px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #dee2e6;
border-radius: 4px;
}
.result-container h3 {
color: #333;
margin-top: 0;
margin-bottom: 10px;
}
.result-container p {
margin: 5px 0;
font-size: 1.1em;
color: #333;
}
Understanding Integers and Their Operations
Integers are fundamental building blocks in mathematics. They are whole numbers (not fractions or decimals) that can be positive, negative, or zero. Examples include -3, 0, 5, 100, and -1000. Unlike natural numbers (which are positive whole numbers starting from 1) or whole numbers (which include 0 and positive whole numbers), integers extend to the negative side of the number line.
Why are Integer Operations Important?
Integers are used extensively in everyday life, science, engineering, and computer programming. From tracking temperatures (positive and negative degrees) and financial balances (credits and debits) to indexing arrays in programming and solving complex mathematical problems, a solid understanding of integer operations is crucial.
Basic Integer Operations
Addition: Combining two or more integers. For example, 5 + (-3) = 2.
Subtraction: Finding the difference between two integers. For example, 7 – 10 = -3.
Multiplication: Repeated addition of an integer. For example, 4 * (-2) = -8.
Division: Splitting an integer into equal parts. Integer division often results in a quotient and a remainder. For example, 10 divided by 3 is a quotient of 3 with a remainder of 1.
Advanced Integer Operations
Beyond basic arithmetic, several other operations are specifically relevant to integers:
Greatest Common Divisor (GCD): The largest positive integer that divides two or more integers without leaving a remainder. For instance, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 (12 = 6 * 2) and 18 (18 = 6 * 3) evenly. GCD is used in simplifying fractions and in cryptography.
Least Common Multiple (LCM): The smallest positive integer that is a multiple of two or more integers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that is a multiple of both 4 (4 * 3 = 12) and 6 (6 * 2 = 12). LCM is essential when adding or subtracting fractions with different denominators and in scheduling problems.
How to Use the Integers Calculator
Our Integers Calculator simplifies these operations for you. Simply enter your first integer and your second integer into the designated fields. Then, click on the button corresponding to the operation you wish to perform: Add, Subtract, Multiply, Divide, GCD, or LCM. The result will be displayed instantly below the buttons.
Examples:
Addition: If First Integer = 15, Second Integer = -7, then Add = 8.
Subtraction: If First Integer = 20, Second Integer = 25, then Subtract = -5.
Multiplication: If First Integer = -6, Second Integer = 3, then Multiply = -18.
Division: If First Integer = 23, Second Integer = 5, then Divide = Quotient 4, Remainder 3.
GCD: If First Integer = 36, Second Integer = 48, then GCD = 12.
LCM: If First Integer = 10, Second Integer = 15, then LCM = 30.
This calculator is a handy tool for students, educators, and anyone needing quick and accurate integer calculations, helping to verify homework, understand number properties, or perform quick computations for programming tasks.