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Prime Factors, HCF and LCM

Highest Common Factor (HCF)

We say that d is a common factor of a and b if d is a factor of both a and b.

We say that d is the highest common factor of a and b if there is no other factor of both a and b that is greater than d.

Notation: HCF(a,b) = “highest common factor of a and b” .

This is also sometimes denoted by GCD(a,b) read as “the greatest common divisor of a and b”.

 

To find the HCF of two numbers:

  • Express each number as a product of prime factors.
  • Choose all the prime factors which are in common in the two numbers.
  • The HCF is the product of the chosen prime factors.

Example

Click the question marks to see the example step by step.

hcf of 16 and 20 is 4

Find HCF( ,).


HCF = 

Exercise

Find the highest common factor (HCF) of each pair of numbers.

Find the HCF of      and 

Working space

HCF =    

<< Prime Factorisation | HCF and LCM Index | Lowest Common Multiple (LCM) >>

 

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