GCF Calculator

Welcome to our Enhanced GCF (Greatest Common Factor) Calculator! This powerful tool helps you quickly find the largest positive integer that divides two numbers without leaving a remainder. Whether you're a student tackling math homework, a teacher preparing lessons, or simply curious about number theory, our calculator is here to assist you.

What is 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 a remainder. Understanding GCF is crucial in various mathematical operations, including simplifying fractions, solving algebraic equations, and more.

How to Use Our GCF Calculator

  1. Enter your first number in the "Enter first number" field.
  2. Enter your second number in the "Enter second number" field.
  3. Click the "Calculate GCF" button to see the result.
  4. Review the step-by-step explanation to understand the calculation process.

Our calculator not only provides the GCF but also shows you the steps involved, making it an excellent learning tool. Try different number combinations to explore fascinating patterns in number theory!

How to Use the GCF Calculator: A Comprehensive Guide

Step-by-Step Instructions

  1. Enter the first number in the "Enter first number" field.
  2. Enter the second number in the "Enter second number" field.
  3. Click the "Calculate GCF" button.
  4. Review the result and the step-by-step explanation.

Math Examples

Let's find the GCF of 24 and 36:

  1. List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  2. List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  3. Identify the common factors: 1, 2, 3, 4, 6, 12
  4. The greatest among these is 12

Therefore, the GCF of 24 and 36 is 12.

Let's find the GCF of 18 and 45 using the Euclidean algorithm:

  1. 45 = 2 × 18 + 9
  2. 18 = 2 × 9 + 0

The last non-zero remainder is 9.

Therefore, the GCF of 18 and 45 is 9.

Let's find the GCF of 17 and 23:

  1. 17 and 23 are both prime numbers.
  2. They have no common factors other than 1.

Therefore, the GCF of 17 and 23 is 1.

Note: When the GCF of two numbers is 1, we say they are coprime or relatively prime.

Pro Tip!

The GCF is particularly useful when simplifying fractions. For example, if you have the fraction 24/36, you can divide both the numerator and denominator by their GCF (12) to get the simplified fraction 2/3.