Find the Gcf Calculator

Greatest Common Factor (GCF) Calculator

Find the highest number that divides all your inputs evenly.

Result:

function calculateGCF() { var input = document.getElementById("numbersInput").value; var resultArea = document.getElementById("gcfResultArea"); var output = document.getElementById("finalOutput"); var steps = document.getElementById("calculationSteps"); // Clean input: split by comma or space, convert to numbers var rawArray = input.split(/[ ,]+/); var numbers = []; for (var i = 0; i 0) { numbers.push(num); } } if (numbers.length < 2) { resultArea.style.display = "block"; output.innerHTML = "Invalid Input"; steps.innerHTML = "Please enter at least two positive integers to find the GCF."; output.style.color = "#e74c3c"; return; } // GCD function using Euclidean Algorithm function findGCD(a, b) { while (b) { var temp = b; b = a % b; a = temp; } return a; } var currentGCF = numbers[0]; var progression = numbers[0]; for (var j = 1; j < numbers.length; j++) { currentGCF = findGCD(currentGCF, numbers[j]); } resultArea.style.display = "block"; output.style.color = "#27ae60"; output.innerHTML = "GCF = " + currentGCF; var stepText = "The Greatest Common Factor of " + numbers.join(", ") + " is " + currentGCF + "."; stepText += "This means " + currentGCF + " is the largest whole number that can divide all of these values without leaving a remainder."; steps.innerHTML = stepText; }

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides two or more numbers without leaving a remainder. Identifying the GCF is a fundamental skill in arithmetic and algebra, essential for simplifying fractions and factoring polynomials.

How to Find the GCF

There are several methods to determine the GCF of a set of numbers. This calculator primarily utilizes the Euclidean Algorithm, which is the most efficient mathematical approach. Here are the most common manual methods:

• Listing Factors: You list all factors of each number and identify the largest one they all share. For example, for 12 (1, 2, 3, 4, 6, 12) and 18 (1, 2, 3, 6, 9, 18), the GCF is 6.
• Prime Factorization: You break each number down into its prime factors. The GCF is the product of the lowest powers of all common prime factors.
• Euclidean Algorithm: You divide the larger number by the smaller number and then divide the divisor by the remainder until the remainder is zero. The last non-zero remainder is the GCF.

Real-World Examples

Numbers	Factors	GCF
24 and 36	Common: 1, 2, 3, 4, 6, 12	12
15 and 25	Common: 1, 5	5
48, 72, and 120	Common: 1, 2, 3, 4, 6, 8, 12, 24	24

Why Use a GCF Calculator?

While finding the GCF of small numbers like 4 and 8 is simple, working with larger numbers or multiple values (like 456, 1024, and 2048) can be time-consuming and prone to manual errors. Our tool provides an instant result, ensuring accuracy for students, teachers, and professionals working in engineering or computer science where modular arithmetic is frequently applied.

Frequently Asked Questions

Can the GCF be 1?

Yes. If two numbers have no common factors other than 1, they are called "relatively prime" or "coprime." For example, the GCF of 9 and 10 is 1.

What is the difference between GCF and LCM?

The GCF is the largest factor that divides numbers, while the Least Common Multiple (LCM) is the smallest multiple that is divisible by the numbers. For 4 and 6, the GCF is 2 and the LCM is 12.