LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING 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. **