.common-factor-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 25px;
border: 1px solid #e0e0e0;
border-radius: 8px;
background-color: #f9f9f9;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
}
.common-factor-calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 26px;
}
.common-factor-calculator-container .input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
}
.common-factor-calculator-container label {
margin-bottom: 7px;
color: #555;
font-weight: bold;
font-size: 15px;
}
.common-factor-calculator-container input[type="number"] {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 16px;
box-sizing: border-box;
}
.common-factor-calculator-container button {
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
font-size: 18px;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
.common-factor-calculator-container button:hover {
background-color: #0056b3;
}
.common-factor-calculator-container .result-section {
margin-top: 25px;
padding: 15px;
border: 1px solid #d4edda;
background-color: #e9f7ef;
border-radius: 5px;
min-height: 50px;
color: #155724;
font-size: 16px;
line-height: 1.6;
}
.common-factor-calculator-container .result-section p {
margin: 5px 0;
}
.common-factor-calculator-container .result-section strong {
color: #004085;
}
.common-factor-calculator-container .article-content {
margin-top: 30px;
padding-top: 20px;
border-top: 1px solid #eee;
color: #333;
line-height: 1.7;
}
.common-factor-calculator-container .article-content h3 {
color: #007bff;
margin-top: 20px;
margin-bottom: 15px;
font-size: 22px;
}
.common-factor-calculator-container .article-content p {
margin-bottom: 10px;
}
.common-factor-calculator-container .article-content ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 10px;
}
.common-factor-calculator-container .article-content ol {
list-style-type: decimal;
margin-left: 20px;
margin-bottom: 10px;
}
function getFactors(num) {
var factors = [];
if (num <= 0) return [];
for (var i = 1; i * i <= num; i++) {
if (num % i === 0) {
factors.push(i);
if (i * i !== num) {
factors.push(num / i);
}
}
}
factors.sort(function(a, b) { return a – b; });
return factors;
}
function calculateCommonFactors() {
var num1Input = document.getElementById("number1").value;
var num2Input = document.getElementById("number2").value;
var num1 = parseInt(num1Input);
var num2 = parseInt(num2Input);
var resultDiv = document.getElementById("commonFactorResult");
resultDiv.innerHTML = "";
if (isNaN(num1) || isNaN(num2) || num1 <= 0 || num2 <= 0 || !Number.isInteger(num1) || !Number.isInteger(num2)) {
resultDiv.innerHTML = "Please enter two positive whole numbers.";
return;
}
var factors1 = getFactors(num1);
var factors2 = getFactors(num2);
var commonFactors = [];
for (var i = 0; i 0) {
var gcf = commonFactors[commonFactors.length – 1];
resultDiv.innerHTML += "The factors of " + num1 + " are: " + factors1.join(", ") + "";
resultDiv.innerHTML += "The factors of " + num2 + " are: " + factors2.join(", ") + "";
resultDiv.innerHTML += "The common factors of " + num1 + " and " + num2 + " are: " + commonFactors.join(", ") + "";
resultDiv.innerHTML += "The Greatest Common Factor (GCF) is: " + gcf + "";
} else {
resultDiv.innerHTML += "There are no common factors other than 1 for " + num1 + " and " + num2 + ".";
resultDiv.innerHTML += "The Greatest Common Factor (GCF) is: 1";
}
}
// Run calculation on page load with default values
window.onload = calculateCommonFactors;
Common Factor Calculator
Understanding Common Factors
In mathematics, a factor of a number is an integer that divides the number evenly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
A common factor of two or more integers is an integer that divides each of them without leaving a remainder. In simpler terms, it's a number that is a factor of all the numbers in a given set.
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest of these common factors. It's a fundamental concept used in various mathematical operations, such as simplifying fractions and solving algebraic equations.
How to Find Common Factors
To find the common factors of two or more numbers, you typically follow these steps:
- List all factors for each number: Determine every positive integer that divides each number evenly.
- Identify common factors: Compare the lists of factors and pick out all the numbers that appear in every list.
- Determine the GCF: From the list of common factors, the largest one is the Greatest Common Factor.
Example: Finding Common Factors of 24 and 36
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
By comparing these lists, we can see the numbers that appear in both:
- Common Factors: 1, 2, 3, 4, 6, 12
The largest number in this list is 12, so the Greatest Common Factor (GCF) of 24 and 36 is 12.
Why are Common Factors Important?
Common factors and the GCF have several practical applications:
- Simplifying Fractions: To reduce a fraction to its simplest form, you divide both the numerator and the denominator by their GCF.
- Algebra: Factoring expressions often involves finding the GCF of terms.
- Problem Solving: They are useful in various word problems involving dividing items into equal groups or arranging objects.
- Least Common Multiple (LCM): The GCF is closely related to the LCM, another important concept for adding and subtracting fractions.
Our Common Factor Calculator simplifies this process, allowing you to quickly find all common factors and the GCF for any two positive integers.