HCF – Highest Common Factor

The highest possible number that divides both numbers completely is the Highest Common Factor (HCF) of two numbers। Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF)।

The HCF of two numbers can be found in a variety of ways। The prime factorization method is one of the quickest ways to find the HCF of two or more numbers। Examine the different facets and features of HCF to learn about its world। Find answers to questions like what is the highest common factor for a group of numbers, easy methods to calculate HCF, HCF by division method, its relationship with LCM, and more interesting facts about them।

The highest number among all the common factors of the specified numbers is the HCF of two or more numbers। Simplely, the Highest Common Factor (HCF) of two natural numbers x and y is the greatest number that can divide both x and y। Using the numbers 18 and 27, we can understand the HCF definition। 1, 3, and 9 are the common factors of 18 and 27। The highest number among these numbers is 9। , HCF 18 and 27 is 9 HCF (18, 27) = 9 is the notation for this। To understand this idea, see the following figure।

                                     HCF of 18 and 27

                                                                                Factors of 18 are: 1,2,3,6,9,18

                                                                                Factors of 27 are: 1,3,9,27

                                                                                                      Common Factors: 1,3 and 9

HCF Examples: Based on the previous HCF definition, the HCF of several numbers can be listed as follows:

HCF (60, 40) = 20

HCF (150, 50) = 50

HCF (17, 89) = 1

 

Prime Factorization using HCF

We employ the following procedures to determine the HCF of numbers using the prime factorization method. Let’s use the example provided below to better grasp this approach.

Step1 : determine which of the supplied numbers are common prime factors.
Step 2: To find the HCF of those integers, multiply the common prime factors with the least or smallest power.

Example: Find the HCF of 60 and 90.

Solution:

The prime factors of 60 = 2 × 2 × 3 × 5 or 2² × 3 × 5

The prime factors of 90 = 2 × 3 × 3 × 5 or 2 × 3² × 5.

Now, the HCF of 60 and 90 will be the product of the common prime factors that have the least powers, which are, 2, 3, and 5. So, HCF of 60 and 90 = 2 × 3 × 5 = 30