# HCF (GCD) : Definitions and Basics

In this post we will understand meaning of HCF/GCF and its significance in competition exams. After that we will also see some examples of HCF calculation for your conceptual understanding.

## What is the full form of HCF?

Full form of HCF is Highest Common Factor.
HCF is also known as GCD or GCF
GCD => Greatest Common Divisor
GCF => Greatest Common Factor

Hence HCF, GCD, GCF all mean the same thing.
Now we know the full form of HCF, its time to understand what does HCF specify and how does it help to solve maths problems.

## What does HCF mean?

HCF of any two numbers is basically the largest numbers which can fully divide the given two numbers.
Let us understand the concept with example:

### 1. HCF (12,15) is 3

This means that 3 is the largest number which can fully divide both 12 and 15

### 2. HCF (90, 150, 225) is 15

It means that 15 is the largest possible number which will fully divide 90, 150 and 225 leaving 0 remainder

### 3. HCF (17, 23, 29 ) is 1

Hence 1 is the largest number that will fully divide 17, 23, 29 leaving 0 remainder.

## How to calculate HCF/GCD?

In the below section we will try to understand how to find the greatest common factor of given numbers with the help of some examples.

### (01) we will start by calculating the HCF of 12 and 15.

In order to calculate GCF, do the following steps:

Step 1: Do the prime factorization of each number
Prime Factors of 12 and 15 are:
12 => 2 * 2 * 3
15 => 3 * 5

Step 2: Now find the factors which are common among the two numbers

For the numbers 12 & 15, you can see that number 3 is common factor for both 12 and 15.

So, number 3 is the only common divisor between the two and hence is the HCF (largest number which can fully divide both 12 and 15)

Hence HCF (12 & 15) ==> 3

### (02) Find the HCF of 150, 210 and 375

Step 1
Do the Prime Factorization of Each number
150 = 2 * 3 * 5 * 5
210 = 2 * 3 * 5 * 7
375 = 3 * 5 * 5 * 5

Step 2:
Now find the common factor among each of the numbers
After analyzing you will that number 3 and 5 are the factors which are common among all the three numbers

Hence the HCF (150, 210, 375 ) is => 3 * 5 => 15

### (03) Find HCF of 15, 25 and 30

Step 01:
Find prime factors of numbers 15, 25 and 30
15 => 3 * 5
25 => 5 * 5
30 => 2 * 3 * 5

Step 02:
Now find the common factors present in each number
After analysis you will find that 5 is the number which is present in all three given number

Hence HCF (15, 25, 30) is 5

I hope with the help of three examples you have now understood how to calculate GCF of any given numbers. My request is to remember the concept as there are lots of application based question which is asked in the competition examinations.

HCF Explanation in English

HCF Explanation in Hindi

I hope now you have understood the concept of highest common factor, now its time to solve some of the common questions asked in exams. These questions are elementary in nature and will help you set the basic clear for this topic.

### (01) What is the gcf of 24 and 36

Step 1:
We have to find the prime factorization of number 24 and 36
24==> 2 * 2 * 2 * 3
36 ==> 2 * 2 * 3* 3

Step 2:
Now look out for factors which are common among the given numbers
Here the common numbers are ==> 2 * 2 * 3 ==> 12

Hence HCF (24,36) is 12

### (02)What is the GCF of 75 and 30

Step 1:
Find the prime factors of number 75 and 30
75==> 3 * 5 * 5
30==> 2 * 3 * 5

Step 2:
Now find the common factors among the two numbers
On analysis you will see that ==> 3 * 5 are the common factors

Hence HCF (75, 30) is 15

### (03) What is the GCF of 36 and 54

Step 1:
Find the prime factors of 36 and 54
36==> 2 * 2 * 3 * 3
54==> 2 * 3 * 3 * 3

Step 2:
Find the common factors among the two numbers
After analyzing the numbers you will see that ==> 2*3*3 are the common numbers

Hence HCF (36, 54) is 18

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