Greatest Common Factor Calculator

Understanding Greatest Common Factor (GCF)

What is the Greatest Common Factor?

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the numbers without a remainder. It's a fundamental concept in number theory and has various applications in mathematics and computer science.

Formula for GCF

The Euclidean algorithm is an efficient method for computing the GCF of two numbers. It can be expressed as:

\[GCF(a, b) = GCF(b, a \bmod b)\]

Where:

• \(a\) and \(b\) are the two numbers
• \(a \bmod b\) represents the remainder when \(a\) is divided by \(b\)

Calculation Steps

Let's find the GCF of 48 and 18:

1. Start with \(a = 48\) and \(b = 18\)
2. \(GCF(48, 18) = GCF(18, 48 \bmod 18) = GCF(18, 12)\)
3. \(GCF(18, 12) = GCF(12, 18 \bmod 12) = GCF(12, 6)\)
4. \(GCF(12, 6) = GCF(6, 12 \bmod 6) = GCF(6, 0)\)
5. Since \(b = 0\), the GCF is \(a = 6\)

Example and Visual Representation

This diagram illustrates that 6 is the Greatest Common Factor of 48 and 18.