Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is a fundamental concept in number theory and arithmetic. It refers to the largest positive integer that divides two or more integers without leaving a remainder. The HCF is particularly useful for simplifying fractions, solving problems involving ratios, and understanding the properties of numbers.

How to Find HCF of 3 Numbers?

To find the HCF of 3 numbers, identify their prime numbers and multiply the common prime factors.

Steps To find the Highest Common Factor (HCF) of three numbers:

Step 1: Find the prime factors of each number.

Step 2: Identify the common prime factors among the three numbers.

Step 3: Multiply the common prime factors.

Step 4: Product obtained is the HCF of the three numbers.

Example: Let’s say we want to calculate the HCF of 12, 18, and 24.

Solution:

Find the prime factors of each number:

• Prime factors of 12: 12 = 2×2×3
• Prime factors of 18: 18 = 2×3×3
• Prime factors of 24: 24 = 2×2×2×3

Identify the common prime factors:

The common prime factors among 12, 18, and 24 are 2 and 3.

Multiply the common prime factors:

2×3 = 6

The product obtained is the HCF of the three numbers:

Therefore, the HCF of 12, 18, and 24 is 6.

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