LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

H.C.F - PRIME FACTORIZATION METHOD

**Finding H.C.F Via Prime Factorization Method -**

**HCF**

**1. PRIME FACTORIZATION METHOD : In this method**

**§ STEP 1.) First we find the prime factors
of the given numbers separately
by factorization.**

**§ STEP 2.) Then we underline the common prime factors of the numbers and write it down.**

**§ STEP 3.) We multiply the common prime factors**

**§ STEP 4.) The product of these common prime factors is the H.C.F of the given numbers.**

**SOLVED EXAMPLE:**

**Q. Find the HCF using PRIME FACTORIZATION METHOD.**

**210, 360, 150**

**Ans.)**

__STEP 1.)__ Write the Prime Factors and do the red color the Common Factors

**210
= 2 x 3 x 5 x 7 x 1 **

** 360 = 2 x 2 x 2 x 3 x 3 x 5 x 1**

**150 = 2 x 3 x 5 x 5 x 1**

**STEP 2.)**

**Common factors = 2 x 3 x 5 x 1 (Multiply
the Common Factors)**

**STEP 3.)**

**H.C.F = 30 (The product is the H.C.F)**

**STEP 4.)**

**Answer: The HCF of 210, 360 and 150 is 30. (Ans.)**

**Important Note -**

**Two numbers are called Co-prime if their HCF is 1. **

__Example:__ 12 and 25

**Factors of 12 are 1, 2, 3, 4, 6 and 12.**

**Factors of 25 are 1, 5 and 25. Common Factor is 1**

**∴ HCF
is 1**

**So, 12 and 25 are Co-prime.**