CLASS-5
HIGHEST COMMON FACTOR (HCF)

HIGHEST COMMON FACTOR (HCF) OF THREE NUMBERS

1) Suppose there are three numbers these are 45, 25, 35. We need to find the Highest Common Factors of these numbers –

Factors of 45 are -  5 x 9 = 45  

                       3 x 15 = 45 

                       45 x 1 = 45

Factors of 25 are -  5 x 5 = 25   

                       25 x 1 = 25

Factors of 35 are – 5 x 7 = 35

                      35 x 1 = 35  

Factors of 45 = 1, 3, 5, 9, 15, 45

Factors of 25 = 1, 5,25

Factors of 35 = 1, 5, 7, 35

So, the highest common factor of these three numbers is 5 .

 2) Suppose there are three numbers these are 24, 48, 36. We need to find the Highest Common Factors of these numbers –

Factors of 24 are -  4 x 6 = 24                               

                        3 x 8 = 24 

                       12 x 2 = 24     

                       24 x 1 = 24    

Factors of 48 are -   6 x 8 = 48  

                        12 x 4 = 48                                   

                        16 x 3 = 48                               

                        24 x 2 = 48                             

                        48 x 1 = 48        

Factors of 36 are – 4 x 9 = 36

                     12 x 3 = 36  

                      6 x 6 = 36

                     18 x 2 = 36

                     36 x 1 = 36

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 35

So, the common factor of these three numbers are  1, 2, 3, 4, 6, 12

So, from the above common factors the highest common factor (HCF) is 12.      (Ans.)

FINDING HCF BY DIVISION METHOD -

1) Find HCF of 20, 30, 40

HCF of the above three numbers should be a product of the common factors 2 & 5.

So, HCF of 20 , 30 & 40 is 2 x 5 = 10.

 

2) Find HCF of 24, 48, 36       

HCF of the above three numbers should be product of the common factors 2, 2 & 3..

So, HCF of 24, 48 & 36 is 2 x 2 x 3 = 12. (Ans.)

HCF by Listing Factorization

This process is to find factorization through listing of common prime factors of given numbers.

Find the HCF of three numbers  18, 27, 24

So, prime factorization of  18 = 2 x 3 x 3

     prime factorization of  27 = 3 x 3 x 3

     prime factorization of  24 = 2 x 2 x 2 x 3

 

common prime factor  =  3         (Ans.)