The Greatest Common Factor (GCF) Calculator helps you quickly find the largest number that divides two or more numbers evenly. The GCF is also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF). This tool is useful for simplifying fractions, solving math problems, and understanding number relationships.

What is GCF?

The GCF of two or more numbers is the biggest number that divides all the given numbers without leaving a remainder.

How to Find GCF

You can find GCF using methods like:

• Prime Factorization
• Listing Factors
• Division Method (Euclidean Algorithm)

Formula (Euclidean Algorithm)

GCF(a, b) = GCF(b, a mod b)

Where:

• a and b are the given numbers
• a mod b is the remainder when a is divided by b
• The process repeats until the remainder becomes 0
• The last non-zero remainder is the GCF

Examples

Example 1:

Find GCF of 12 and 18
Factors of 12 → 1, 2, 3, 4, 6, 12
Factors of 18 → 1, 2, 3, 6, 9, 18
Common factors → 1, 2, 3, 6
GCF = 6

Example 2:

Find GCF of 20 and 30
Common factors → 1, 2, 5, 10
GCF = 10

Example 3:

Find GCF of 8 and 28 using Euclidean Algorithm:
28 mod 8 = 4
8 mod 4 = 0
Result: GCF = 4

This calculator is perfect for students, teachers, and anyone needing quick factorization results.