HCF Full Form

HCF full form is the Highest Common Factor. But, are you aware of the process used in finding HCF of a number in Mathematics? Don’t worry. Read the article below to know the details regarding HCF full form, methods to find HCF of a given number and a lot more. 

What is HCF Full Form?

HCF full form is the Highest Common Factor. The highest factor or the number that divides any pair of two or more numbers evenly is known as the HCF or highest common factor. The Greatest Common Measure (GCM) and the Greatest Common Divisor (GCD) are other names used for HCF.

HCF can be accessible by using two or more numbers. For each pair of integers that can evenly or completely divide the given numbers, it is the most efficient divisor.

For example, 12 is the greatest number that can divide 24 and 60 completely, making it the highest common factor of these two numbers.

Methods to Find HCF

We can find the HCF of any given numbers by using two specific methods:

• By prime factorization method

• By division method

The methods and details of two methods are discussed below:

HCF By Prime Factorization Method

To find the HCF of any given numbers using the prime factorisation method, follow the steps below:

• Step 1: Write down each number as a product of its prime factors. This method is called the ‘prime factorization’ method
• Step 2: Now list the ‘common factors’ of both the numbers
• Step 3: The product of all common prime factors is the known as HCF (use the lower power of each common factor)

Examples of HCF

Example 1: Find the HCF of 60 and 75

Solution:

Example 2: Find the HCF of 36, 24 and 12

Solution:

Example 3: Find the HCF of 36, 27 and 80.

Solution:

How to Find HCF by Division Method?

One of the most important methods of finding the highest common factor (HCF) is by prime factorization method. HCF can also be found by another method known as the ‘division method’. Basically, the division method is nothing but dividing the given numbers, at the same time to get the common factors between them. Following are the steps mentioned to solve the problems of HCF using the division method:

• Step 1: Write down the given numbers horizontally in a sequence, by separating them with commas
• Step 2: Find the smallest prime number which can divide the provided number. It should exactly divide the given numbers and write on the left side
• Step 3: Now, write the quotients
• Step 4: Continue the process until you reach the stage, where there is no coprime number left
• Step 5: We will get the ‘common prime factors’ as the factors on the left-hand side that divide all the numbers precisely. The product of these common prime factors is called as the  HCF of the given numbers

Let us understand the above-mentioned steps to find the HCF by ‘division method’ with the help of examples below

Example 1: Evaluate the HCF of 30 and 75

The above mentioned prime factors on the left side, divide all the numbers completely. Therefore, they are considered as common prime factors. For the numbers remaining at the bottom, there is no common prime factor.

Therefore, the HCF is, 3 × 5 = 15

Example 2: Find out HCF of 36 and 24

HCF = 2 × 2 × 3 = 12

Example 3: Find out HCF of 36, 12, 24 and 48

So, the HCF is  2 × 2 × 3 = 12

How to Find HCF by Shortcut Method?

Steps to find the HCF of any given set of numbers using the shortcut method are:

• Step 1: At first, divide the larger number by the smaller number, such as

Larger Number/Smaller Number

• Step 2: Divide the divisor of the large number/smaller number by the remainder left i.e Divisor of step 1/Remainder

• Step 3: Again divide the divisor of step 2 by the remainder that is Divisor of step 2/Remainder

• Step 4: Repeat the same process until the remainder is zero
• Step 5: The divisor of the last step will be the HCF

How to Find the HCF of Three numbers?

Find the steps to calculate the HCF of the 3 numbers and the rest of the steps are given below:

Moreover, the above steps can also be used to find the HCF of more than 3 numbers.

Methods to Find the HCF of Four Numbers

The simple and easy steps to find the HCF of 4 numbers are given below:

• Initially, divide the four numbers into pairs of two
• Find the HCF of the pair of two numbers
• Then, find the HCF of HCFs calculated in the above step
• The obtained HCF will be the required HCF of 4 numbers

What are the Major Properties of HCF?

The major properties of HCF are given below:

• HCF of two or more numbers is the one that divides the given numbers, precisely
• The HCF of prime numbers is always equal to 1
• HCF is always less than or equal to the provided numbers