# HCF Methods of Calculation and Formula

In this post we will discuss different methods for HCF calculation. Choose the one which you feel comfortable solving but please don’t get confused with the choices as it may only disturb your preparation.
Just check all the methods and select the one which suits your temperament

## HCF using Prime Factorization Method

This is the basic and simplest method to calculate HCF of numbers. If you are weak in maths and your love for maths is newly founder, i will suggest to practice this method.

In prime factorization method, we will calculate the prime factors of numbers given then then take out the factors which are common among all the numbers.
The above explanation may seem complex but don’t worry we will understand the concept with the help of examples

### (1) Find the HCF of 12, 15, 18 and 27 using Prime Factorization Method

Step 1:
Find Prime Factors of each number given

Here are the prime factorization of all the numbers
12= 2 * 2 * 3
15= 3 * 5
18= 2 * 3 * 3
27= 3 * 3 * 3

Step 2:
Take out the common factor among all the numbers given

From the above illustration you can see that 3 is the only common number among all.
Hence 3 is the HCF of above numbers
HCF (12, 15, 18 , 27) =3

### (02) Find the HCF of 20, 28 and 36 using Prime Factorization Method

Step 1:
Find Prime Factors of all the given numbers

From above illustration we can see how to calculate prime factors of each number. So the prime factors are:
20=> 2 * 2 * 5
28=> 2 * 2 * 7
36=> 2 * 2 * 3 * 3

Step 2:
Now we have to select the factors which are common among all three numbers

From the above illustration we can see that 2 * 2 are the common factors
So HCF (20, 28, 36) => 2 * 2 => 4

### (03) Find HCF of 32, 36, 40, 42 using Prime Factorization Method

Step 1: Calculate Prime Factorization of each numbers

From the above illustration you can see we have calculated the prime factors of each numbers
32 => 2 * 2 * 2 * 2 * 2
36 => 2 * 2 * 3 * 3
40 => 2 * 2 * 2 * 5
42 => 2 * 3 * 7

Step 2:
Now we have to select the factors which are common among all three

Here you can see that 2 is the only common number among all number present
Hence HCF (32,36,40,42) ==> 2

HCF explanation in English

HCF explanation in Hindi

## Method 2: HCF using Division Method

In this method we will take all the number and try to divide it with the common factors present until no commonality is left between the numbers.
we will study this method with the help of examples

### (01) Find HCF of 54, 108 and 144 using Division Method

Step 1:
Take out the common factors until no common prime factor exits between the numbers

a. we will start with number 2 as all the numbers 54, 108, 144 is divisible by 2.
we will get 27, 54 and 72 as quotient

b. Now we cannot divide 27, 54 and 72 with number 2 again as 27 is not divisible
Please mind that we have to select numbers which will divide all the number present
So now we will divide 27, 54 and 72 with number 3 as all the number is divisible leaving 9, 18, 24 as quotient

c. Now again divide 9, 18 and 24 with number 3 as all are divisible
We get quotient 3, 6, 8

d. Now all 3, 6, 8 are not divisible by any one number
Try with number 3 and you will see that 8 is not divisible.
Now you have reached a point where you will not find any number which can divide all the number present. At this point you have to stop and calculate the HCF

STEP 2:
HCF (54, 108, 144) = 2 * 3 * 3 = 18
Hence 18 is the HCF

### (02) Find the HCF of 52, 96 and 116 using Division Method

Step 1:
Take out the common factors until no common prime factor exits between the numbers

a. we will divide the numbers with 2 and get 26, 48 and 58 as quotient

b. Now again we will divide 26, 48 and 58 with number 2 to get 13, 24 and 29 as quotient left

c. The numbers 13, 24 and 29 have no common link between them.
Meaning that there is no number which can divide 13, 24 and 29, so stop the process here

d. HCF (52, 96, 116) = 2 * 2 ==> 4

### (03) Find the HCF of 120, 220 and 360 using Division Method

Step 1:
Take out the common factors until no common prime factor exits between the numbers

a. we will divide the number with 2 to get quotient 60, 110, 180
b. Again divide the numbers with 2 to get quotient 30, 55 and 90
c. Divide the numbers with 5 to get 6, 11, and 18
d. The numbers 6, 11 and 18 cannot be further divide by any number

So HCF (120, 220, 360) is 20

HCF Division Method (English)

HCF Division Method (Hindi)

## Method 3: HCF using Shortcut method

This method is least time consuming for HCF calculation. So if you are preparing for competition exams like GMAT, CAT, CMAT, SSC-CGL, SSC-CHSL, NMAT, NABARD, SBI-PO, SBI-Banking, IBPS etc, this method is ideal for you.

The only disadvantage is that in order to use this method you have to invest lot of time to practice the process. Now without wasting any time, let us understand the method with the help of examples

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

Step 1:
Find the difference between the numbers. For this question, there are three possibilities:
25 – 15 = 10
30 – 25 = 5
30 -15 = 15

Step 2:
Select the smallest number among the difference produced
In the above calculation we got three numbers 10, 5 and 15. Among these three number we will select number 5 which is the smallest.

Step 3:
Find the factors of smallest number and check whether it divide all the number given in question aka (15, 25, 30)

Factors of number 5 can be displayed as
1 * 5

Both 1 and 5 are the factors of 5
a. Check whether 5 fully divides (15, 25 and 30)
Yes it fully divide the number and thus is the HCF

So, HCF (15, 25, 30) is 5

### (02) Find the HCF of 24, 36 and 60 using shortcut method

Step 1:
Find the difference between all the numbers
36 – 24 = 12
60 – 36 = 24
60 – 24 = 36

Step 2:
Select the smallest number among 12, 24, 36
Here 12 is the smallest number

Step 3:
Find factor of 12
1 * 12
2 * 6
3 * 4
So 1, 2, 3, 4, 6 and 12 are the factors of number 12
Among these factor, one is our HCF.
In order to find the HCF, check if the factor fully divide the number (24, 36 and 60)

Step 4
Find HCF among the calculated factors. Let us start with the highest factor present 12
a. check if 12 fully divides (24, 36 and 60)
Yes it fully divides all the number hence HCF (24, 36 and 60) ==> 12

### (03) Find the HCF 363, 429 and 693 using shortcut method

Step 1:
Find the difference between numbers
429 – 363 = 66
693 – 429 = 264
692 – 363 = 329

Step 2:
Among the difference, select the number which is smallest
Out of 66, 264 and 329, the smallest number is 66

Step 3:
Find the factor of smallest number
1 * 66
2 * 33
3 * 22
6 * 11

Hence the factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
Among these factors, one is the HCF

Step 4:
Find the HCF among the factors

a. Will 66 completely divide 363, 429 and 693
NO, as 66 is even number and 363 is odd number so complete division is not possible

b. Check for second highest number 33
Will 33 fully divide 363, 429, 693
YES..

So no need to check further
HCF (363, 429 and 693) is 33

HCF Shortcut Method (English)

HCF Shortcut Method (Hindi)