Highest Common Factor

Definition:  

The “Highest Common Factor” (HCF) of two or more numbers is the highest or greatest of their common factors.

The HCF of 20, 50, and 30 can also be found by factorization of these numbers as follows,

Therefore, 

                       20 = 2 x 2 x 5 
                       50 = 2 x 5 x 5 
                       30 = 2 x 3 x 5

The common factors of 20, 50 and 30 are 2 and 5. 

Thus HCF of 20, 50, and 30 is 2 x 5 = 10.

1.              Find the HCF of 18 and 48?

The HCF of 18 and 48 can found by factorization of these numbers as follows,

Therefore,

                        18 = 2 x 3 x 3

                        48 = 2 x 2 x 2 x 2 x 3

The common factors of 18 and 48 are 2 and 3. 

Thus HCF of 18 and 48 is 2 x 3 = 6.

2.              Find the HCF of 12, 45, and 75?

The HCF of 12, 45, and 75 can found by factorization of these numbers as follows,

Therefore, 

                             12 = 2 x 2 x 3

                             45 = 3 x 3 x 5

                             75 = 3 x 5 x 5

 The common factor of 12, 45, and 75 is 3. 

Thus HCF of 12, 45, and 75 is 3 = 3.