# CLASS-7FINDING HCF BY PRIME FACTORIZATION METHOD

Finding HCF By Prime Factorization

We should have express each number as a product of prime numbers, then we will find the common factors of the number and then we will find the product of the common factors, this product is the required HCF.

To find the HCF by Prime Factorization –

Example.1 -

Find the HCF of 56 & 42 via prime factorization

Ans.)   56 = 2 X 28 = 2 X 2 X 14 = 2 X 2 X 2 X 7

42 = 2 X 21 = 2 X 3 X 7 ,

Step.1 – We should express each number as a product of prime numbers

Step.2 – we would like to find the common factor of 56 & 42. Here the obtained common factor of the numbers 56 & 42 is 2 & 7. So, as per the rules the product of 2 & 7 is the HCF of 56 & 42 ;  2 X 7 = 14 is the HCF of the 56 & 42.

Example.2-

Find the HCF of 84 & 112 via prime factorization

Ans.)   84 = 2 X 42 = 2 X 2 X 21 = 2 X 2 X 3 X 7

And,  112 = 2 X 56  =  2 X 2 X 28 =  2 X 2 X 2 X 14

=  2 X 2 X 2 X 2 X 7

Step.1– We should express each number as a product of prime numbers

Step.2– we would like to find the common factor of 84 & 112. Here the obtained common factor of the numbers 84 & 112 is 2, 2, & 7. So, as per the rules the product of 2, 2 & 7 is the HCF of 84 & 112. 2 X 2 X 7 = 28 is the HCF of the 84 & 112.