Find the Greatest Common Factor Calculator

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Greatest Common Factor (GCF) Calculator

Understanding 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 integers without leaving a remainder. It's a fundamental concept in mathematics with various applications, especially in simplifying fractions and factoring algebraic expressions.

What is a Factor?

A factor of a number is an integer that divides the number evenly, meaning with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

How to Find the GCF?

There are several methods to find the GCF:

  1. Listing Factors: List all factors for each number and identify the largest factor common to all. This method is practical for smaller numbers.
  2. Prime Factorization: Find the prime factorization of each number. The GCF is the product of all common prime factors, raised to the lowest power they appear in any of the factorizations.
  3. Euclidean Algorithm: This is an efficient method, especially for larger numbers. It states that the GCF of two numbers does not change if the larger number is replaced by its difference with the smaller number. This process is repeated until one of the numbers becomes zero, and the other number is the GCF. More formally, GCF(a, b) = GCF(b, a mod b) until b is 0.

Using the GCF Calculator

Our Greatest Common Factor Calculator uses the efficient Euclidean Algorithm to quickly determine the GCF of two positive integers. Simply enter your two numbers into the designated fields and click "Calculate GCF". The result will instantly appear below.

Example Calculation: GCF of 48 and 180

Let's find the GCF of 48 and 180 using the Euclidean Algorithm:

  • Divide 180 by 48: 180 = 3 × 48 + 36
  • Now, divide 48 by the remainder 36: 48 = 1 × 36 + 12
  • Next, divide 36 by the remainder 12: 36 = 3 × 12 + 0

Since the remainder is now 0, the GCF is the last non-zero remainder, which is 12. Our calculator would provide this result instantly.

Applications of GCF

  • Simplifying Fractions: To simplify a fraction to its lowest terms, divide both the numerator and the denominator by their GCF.
  • Factoring Polynomials: The GCF is used to factor out common terms from polynomials.
  • Distributing Items: In real-world problems, GCF can help in distributing items into the largest possible equal groups.
function calculateGCF() { var number1Input = document.getElementById("number1").value; var number2Input = document.getElementById("number2").value; var num1 = parseInt(number1Input); var num2 = parseInt(number2Input); var resultDiv = document.getElementById("gcfResult"); if (isNaN(num1) || isNaN(num2) || num1 <= 0 || num2 <= 0) { resultDiv.innerHTML = "Please enter two positive whole numbers."; return; } function findGCD(a, b) { a = Math.abs(a); b = Math.abs(b); while (b !== 0) { var temp = b; b = a % b; a = temp; } return a; } var gcf = findGCD(num1, num2); resultDiv.innerHTML = "The Greatest Common Factor (GCF) of " + num1 + " and " + num2 + " is: " + gcf + ""; }

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