Greatest Common Factor (GCF) Calculator

The Greatest Common Factor (GCF) is the largest positive number that divides into all the numbers in a set without leaving a remainder.

Enter two or more positive numbers, separated by commas or spaces.

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor, or GCF, is the largest whole number that is a factor of two or more other numbers. A "factor" is a number that divides another number exactly, without any remainder.

For example, let's find the GCF of 12 and 18:

  • The factors of 12 are: 1, 2, 3, 4, 6, 12.
  • The factors of 18 are: 1, 2, 3, 6, 9, 18.

The "common factors" are 1, 2, 3, and 6. The "greatest" of these common factors is 6. Therefore, the GCF of 12 and 18 is 6.

GCF vs. GCD vs. HCF

You will often see GCF used interchangeably with GCD (Greatest Common Divisor) or HCF (Highest Common Factor).

There is no difference between them. They are three different names for the exact same mathematical concept:

  • GCF: Common in the US.
  • HCF: Common in the UK, Australia, and India.
  • GCD: Common in higher-level mathematics.

How to Use This GCF Calculator

This tool is designed to be a fast and effective learning aid. Here’s how to use it:

  1. Enter Numbers: In the input box, type the numbers you want to find the GCF for. You must enter at least two numbers, separated by a comma (,) or a space.
  2. Calculate GCF: Click the "Calculate GCF" button. The tool will instantly compute the GCF using the highly efficient Euclidean algorithm.
  3. Review the Steps: The calculator not only gives you the answer but also shows you how to find it yourself. It provides detailed, step-by-step breakdowns using all three common methods:
    • Listing Factors: The simplest method, perfect for small numbers.
    • Prime Factorization: A very common method taught in schools.
    • Euclidean Algorithm: The fastest and most efficient method, especially for large numbers.

GCF Solved Examples

Example 1: Find the GCF of two numbers (24 and 36)

We can use the "Listing Factors" method, which is great for visual learners.

  1. List all factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  2. List all factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  3. Find the common factors: 1, 2, 3, 4, 6, 12
  4. Identify the greatest factor:
    The largest number in the common list is 12.

Result: The GCF of 24 and 36 is 12.

Example 2: Find the GCF of three numbers (20, 50, and 80)

Let's use the "Prime Factorization" method for this one.

  1. Find the prime factors of 20: 20 = 2 × 2 × 5
  2. Find the prime factors of 50: 50 = 2 × 5 × 5
  3. Find the prime factors of 80: 80 = 2 × 2 × 2 × 2 × 5
  4. Find the common prime factors:
    Look for the prime factors that *all three* numbers share.
    • All three lists share one 2.
    • All three lists share one 5.
  5. Multiply the common factors: 2 × 5 = 10

Result: The GCF of 20, 50, and 80 is 10.

Frequently Asked Questions

What is the difference between GCF, GCD, and HCF?

There is no difference. GCF (Greatest Common Factor), GCD (Greatest Common Divisor), and HCF (Highest Common Factor) are different names for the exact same mathematical concept.

Can the GCF be larger than the numbers?

No. The Greatest Common Factor can never be larger than the smallest number in your set. For example, the GCF of 10 and 100 is 10.

What is the GCF of Prime Numbers?

If you are finding the GCF of two distinct prime numbers (like 7 and 13), the result is always 1, because they share no factors other than 1.

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