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A Comprehensive Guide to Homeschooling

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.

 

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

 

 

 

 

 

 

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

 

 

 

 

 

 

 

 

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.