Greatest common factor or highest common factor of any two numbers can be find out using prime factorization gcf.

Steps involved in prime factorization gcf :
1) Find the common factors of the given numbers.
2) Now find the greatest of these common factors.The factors which are present in both the numbers are called common factors.1 is always a common factor. So no need to write 1 as a factor. Example : Find the HCF of 12 and 16 using factors.
Factors of 12 = 1 x 4 x 3
Factors of 16 = 1 x 4 x 4
Common factors are 1, and 4.
Highest common factor is 4 .
So HCF of 12 and 16 = 4 Finding HCF using prime factorization. Example: 1 HCF of 20,28 and 36
Thus,
20 = 2 x 2 x 5
28 = 2 x 2 x 7
36 = 2 x 2 x 3 x 3
The common factor of 20,28 and 36 is 2 ( occuring two times).
So, HCF of 20,28 and 36 is 2 x 2 =4. Example 2 : Find HCF of 24 and 36.
First find the factors of 24 and 36 using prime factorization.
24= 2 x 2 x 2 x 3
36= 2 x 2 x 3 x3
The common factors of 24 and 36 is 2( occuring two times) and 3 (one time).
So, HCF of 24 and 36 is 2 x 2 x 3 = 12. Example 3 : Find the HCF of 11 and 15
First find the factors of 11 and 15 using prime factorization.
11 = 1 x 11
15 = 3 x 5
From the above you can see that there is no common facto. But 1 is always a common factor between any two numbers.
So, HCF of 11 and 15 is 1. Note: The highest common factor (HCF) of two or more given numbers is the highest of their common factors.

Practice on Prime Factorization GCF

Q.1 Find the HCF of the following numbers.
1) 18,40
2) 30,42
3) 60,100 and 120
4) 18,54 and 81
5) 34,102
6) 15,25 and 30
7) 8 and 12
8) 31 and 21
9) 13,17 and 19
10) 160 and 120
Q.2 What is the HCF of two consecutive a) numbers ? even numbers?
Q.3 Which of the following numbers have HCF 1?
a) 12 and 15
b) 30 and 60
c) 19 and 21
d) 27 and 54