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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.

Exercise

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

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