Highest Common Factor Calculator – Cost Calculator

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Highest Common Factor (HCF) Calculator

Enter numbers (separated by commas): Example: To find HCF of 12 and 18, type "12, 18"

The result will appear here.

What is the Highest Common Factor (HCF)?

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the integers without leaving a remainder. In simple terms, it is the biggest number that "fits" perfectly into all the numbers you are analyzing.

Understanding HCF is crucial in mathematics for simplifying fractions, finding common denominators, and solving real-world distribution problems where you need to divide different quantities into equal sections.

How to Calculate HCF

There are three primary methods used to find the HCF of two or more numbers:

1. Prime Factorization Method

In this method, you express each number as a product of its prime factors. The HCF is then the product of the lowest powers of all common prime factors.

2. Listing Factors Method

You list all the factors of each number and identify the largest factor that appears in every list.

3. Division Method (Euclidean Algorithm)

This is the most efficient method for large numbers. You divide the larger number by the smaller number. Then, you divide the divisor by the remainder. This process continues until the remainder becomes zero. The last non-zero divisor is the HCF.

Example Calculation: HCF of 24 and 36

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors are 1, 2, 3, 4, 6, and 12.
The Highest Common Factor is 12.

HCF vs. LCM: What is the Difference?

While HCF is the largest divisor, the Least Common Multiple (LCM) is the smallest multiple that is common to all the numbers. For example, for the numbers 4 and 6:

HCF is 2 (the largest number that divides both).
LCM is 12 (the smallest number that both 4 and 6 divide into).

Practical Applications of HCF

HCF isn't just for textbooks; it is used in various fields:

Tiling: Finding the largest size of square tiles needed to cover a rectangular floor without cutting any tiles.
Inventory: Organizing different products into equal-sized crates or packages.
Music: Calculating rhythms and timing patterns in composition.