# Methods Used to Find HCF of Two or More Numbers

### Hello Friends, In this post we will discuss various " Methods Used to Find HCF of Two or More Numbers "

Let's start the session !

Mainly there are two methods used to find out HCF or GCF of two or more numbers which are as follows :

1. PRIME FACTORIZATION METHOD

Step 1 : Express each number as a product of prime numbers

Step 2 : Multiply the least power of all common prime factors of the required number to get HCF

Let's see with some examples !

Question 1 : Find the HCF of 12, 15 and 24 by prime factorization method

Step 1 :

Prime factors of 12 are 2 and 3 thus 12 can be expressed as 2 x 2 x 3
Prime factors of 15 are 3 and 5 thus 15 can be expressed as 3 x 5
Prime factors of 24 are 2 and 3 thus 24 can be expressed as 2 x 2 x 2 x 3

Step 2 :

Now the common prime factors among 12, 15 and 24 is 3, thus HCF of 12, 15 and 24 is 3

Question 2 : Find the HCF of 30, 45 and 90 by prime factorization method

Step 1 :

Prime factors of 30 are 2, 3 and 5 thus 30 can be expressed as 2 x 3 x 5
Prime factors of 45 are 3 and 5 thus 45 can be expressed as 3 x 3 x 5
Prime factors of 90 are 2, 3 and 5 thus 90 can be expressed as 2 x 3 x 3 x 5

Step 2 :

Now the common prime factors among 30, 45 and 90 are 3 and 5, thus HCF of 30, 45 and 90 is 3 x 5 = 15

Question 3 : Find the HCF of 36, 48 and 72 by prime factorization method

Step 1 :

Prime factors of 36 are 2 and 3 thus 36 can be expressed as 2 x 2 x 3 x 3 = 22 x 32
Prime factors of 48 are 2 and 3 thus 48 can be expressed as 2 x 2 x 2 x 2 x 3 = 24 x 3
Prime factors of 72 are 2 and 3 thus 72 can be expressed as 2 x 2 x 2 x 3 x 3 = 23 x 32

Step 2 :

Now the least power of all prime factors are 22 and 3, thus HCF of 36, 48 and 72 are 22 x 3 = 12

Still any doubts ! Just comment in comment section below, we will try to resolve it as soon as possible

2. DIVISION METHOD

Step 1 : Divide greater number by smaller number.

Step 2 : Divide smaller number by remainder you get in Step 1 continue the cycle till remainder = 0

Step 3 : Divide the next number by divisor which leads to remainder = 0 in Step 2

Let's see with an examples !

Question 4 : Find the HCF of 30, 45 and 90 by division method

Step 1 :

Divide 45 by 30, Remainder = 15

Step 2 :

Divide 30 by 15, Remainder = 0, thus HCF of 30 and 45 is 15

Step 3 :

Now divide 90 by 15, Remainder = 0, thus HCF of 30, 45 and 90 is 15

Still any doubts ! Just comment in comment section below, we will try to resolve it as soon as possible

At last, A special thanks to choose LOUD STUDY.
If you have any doubt or confusion under this topic ” Methods Used to Find HCF of Two or More Numbers “, you can post it in comment box. We will feel proud to help you
Disclaimer : All statements used under this topic ” Methods Used to Find HCF of Two or More Numbers ” is verified from different resources available in legit form