HCF Calculator

Understanding Highest Common Factor (HCF)

What is the Highest Common Factor?

The Highest Common Factor (HCF), 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 HCF

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

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

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 HCF of 48 and 18:

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

Example and Visual Representation

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