<p><em>Omitting details of methods to calculate primes, and methods of factorisation.</em></p>
<h3>Why bother to factorise ?</h3>
<h3>What are its applications ?</h3>

Wow, so much fighting in this thread.
Ironically, this question HAS a major valid answer.
Factorization is actually used heavily in encryption/decryption algorithms, so much so that the RSA regularly conducts competitions wherein the task is to factorize certain large numbers that are multiples of very large prime numbers.
This is, in turn, because several encryption/decryption algorithms are based on the premise that factorization takes a very long time, which (supposedly) makes it difficult and/or impractical to crack certain encryption/decryption algorithms given the assumption that the hacker/cracker does not have access to public/private keys.
Factorization algorithms can then be used to verify just how strong any given encryption/decryption algorithm is.