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Highest Common Factor – HCF


What is highest common factor?

The largest common factor of two or more numbers is called the highest common factor (HCF).

 

Other names for highest common factor

Greatest common divisor or greatest common factor (GCF)

 

 

Explanation 1:

 

Find the HCF of 12 and 16

 

Step 1:

First find the factors of numbers given, which means;

 
List all the factors of 12 and 16
 

Number

Factors

12

1 , 2 , 3 , 4 , 6 , 12

16

1 , 2 , 4 , 8 , 16

 

 

 

 

 

Step 2:

Group the common factors.

 

What are common factors?

Common factors are the factors that are found in both lists of factors.

 

Number

Factors

12

1 , 2 , 3 , 4 , 6 , 12

16

1 , 2 , 4 , 8 , 16

 

 

 

 

 

So, the common factors of 12 and 16 are 1 , 2 and 4.

 

Step 3:

Now choose the highest factor of the common factors.

 

1 , 2 , 4

 

It is 4.

 

Therefore, the HCF of 12 and 16 is 4.

 

Explanation 2:

 

Find the HCF of 15 , 30 and 60

 

Step 1:

List all the factors of 15 , 30 and 60

 

Number

Factors

15

1 , 3 , 5 , 15

30

1 , 2 , 3, 5, 6 , 10 , 15 , 30

60

1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60

 

 

 

 

 

 

Step 2:

Group the common factors.

 

Number

Factors

15

1 , 3 , 5 , 15

30

1 , 2 , 3, 5, 6 , 10 , 15 , 30

60

1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60

 

 

 

 

 

So, common factors of 15 , 30 and 60 are 1 , 3 , 5 and 15.

 

Step 3:

Now choose the highest of the common factors.

 

1 , 3 , 5 , 15

 

It is 15.

 

Therefore the HCF of 15 , 30 and 60 is 15.

 

Hope you have learned the way to find the highest common factor (HCF) or the greatest common factor (greatest common divisor). Try the HCF Quiz.