Shell Script to Find Prime Factors of a Number

Shell Script to Find Prime Factors of a Number 

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization. Example: The prime factors of ! are ", , # and $$: ! % " &  & # & $$  There is no other possible set of prime numbers that can be multiplied to ma'e !.  (ou can find prime factors of a number using )*I+-inux utility factor. This is a very convenient and cool )*I+ command. ere is its syntax: / factor !: "  / factor "$"$011:

! # $$ "$"$011 $$ $$ $ $0 1$

 2any 3lgorithms have been devised for determining the 4rime factors of a given number. They vary quite a bit in sophistication and complexity. It is very difficult to build a general5purpose algorithm for this computationally 6hard6 problem, so any additional information which is 'nown about the number in question or its factors can often be used to save a large amount of time.  ere I am providing a shell script to find prime factors of a positive integer. This script does most factorizations within a second. In the worst case scenario 7for some large semi5primes with

more than 85digit factors9 factorization will ta'e a couple of minutes to hours.

;binbash  <=>I4T: primefactors.sh  )<3?E : primefactors.sh @4ositive IntegerA  4)>4B
primenumber /counter$ FF factorchec' /$ /counter$ FF brea' done O factorchec'79 K prime%/" newnum%/$ remainder%/77newnumNprime99 if C /remainder 5eq ! D then printf 6Ndx6 /prime newnum%/77newnumprime99 primefind /newnum " return else let prime primefind /newnum /prime fi O   2ain  echo 5n 64rime actors of /$: primefind /num " printf 6Qb Qn6  Qb is used for removing last x. OUTPUT:

CrootRvenu D sh primefactors.sh )sage: scriptname @positive integer%66A CrootRvenu D sh primefactors.sh "$"$0101 4rime actors of "$"$0101: $!$x"$!!01 CrootRvenu D sh primefactors.sh "$"$01 4rime actors of "$"$01: SSxS10 >unning time of script doesnPt depend on number,it depends on number of factors, more factors less time and less factors more time. CrootRvenu D time sh primefactors.sh 0000000000000000 4rime actors of 0000000000000000: xx$$x$1x1x$!$x$1x#"# real user sys

!m$.S#s !m$.""#s !m!.!0$s

CrootRvenu D time sh primefactors.sh 00000000000# 4rime actors of 00000000000#: #x"#$x$$xS#$10 real user sys

$m".$!#s $m".88s !m.$0"s

CrootRvenu D time sh primefactors.sh 00000000!!!!!!!!!

4rime actors of 00000000!!!!!!!!!: "x"x"x"x"x"x"x"x"xxx#x#x#x#x#x#x#x#x#x$$x1 x$!$x$1 real user sys

!m!.#Ss !m!.#!s !m!.!#s