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Highest Common Factor – HCF


 

What is Highest Common Factor – HCF?

The largest common factor of two or more numbers is called the Highest Common Factor – HCF.

 

Other names for Highest Common Factor – HCF

Greatest Common Factor

 

 

Explanation 1:

 

Find the HCF of 12 and 16

 

Step 1:

 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 highest common factor 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 highest common factor of 15 , 30 and 60 is 15.