Fundamental Theorem Of Arithmetic

The Fundamental Theorem of Arithmetic says that every composite number can be factorised as a product of primes.

It says that givenany composite number it can be factorised as a product of prime numbers in a
‘unique’ way, except for the order in which the primes occur. That is, given any composite number there is one and only one way to write it as a product of primes, as long as we are not particular about the order in which the primes occur. So, for example, we regard 2 × 3 × 5 × 7 as the same as 3 × 5 × 7 × 2, or any other possible order in which these primes are written. 

Example:

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

Solution:

We have : 6 = 21 × 31 and 20 = 2 × 2 × 5 = 22 × 51.

You can find HCF(6, 20) = 2 and LCM(6, 20) = 2 × 2 × 3 × 5 = 60, as done in your
earlier classes.