How to find HCF

H.C.F. can be found by two methods- Prime factorization and the Long Division Method. Lets take an example to understand each one of them.

example to  find HCF of 108 and 152

1. Prime Factorization: First we have to find the prime factors of the number. 

       

Now, in terms of prime factors we can write the numbers 108 and 152 as 

108 = 2 x 2 x 3 x 3 x 3
152 = 2 x 2 x 2 x 19

Now circle the prime numbers that are common to both

Writing once the numbers that are common to both and multiply them to get the HCF.

We can see that (2 x 2) is common to both,

Hence, HCF = 2 x 2 = 4

2. Long Division Method

For Long Division,

1. Take the smaller number as the divisor and divide the larger number.

2. If the remainder is zero then the divisor itself is the HCF of both the numbers, otherwise go to step 3

3. If we get a non zero remainder, then take the remainder as the divisor and the divisor from the first step is taken as the dividend. Again divide the numbers . If we get zero as remainder then the divisor from this step is the required HCF, else repeated step3, till we get zero as the remainder.

 The HCF of 108 and 152 is obtained using the long division method as:

Since 4 is the last divisor that resulted in a zero remainder. Therefore, 4 is the HCF of 108 and 152.


To know the methods for finding LCM read :
       

•                          How to find LCM of given numbers