Solver Find factors of any number

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Algebra: Divisibility and Prime Numbers

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Source code of 'Find factors of any number'

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==section input
Find all factors of *[input a=24].

==section solution
perl
        my $orig_a = $a; 
        #my $b = $cgi->param( 'b' ); 
        unless( $a =~ /^\d+$/ ) { 
          print "Natural number expected instead of '$a'.\n"; 
          return; 
        } 
 
        if( $a == 0 || $a == 1 ) { 
          print "$a is a special case and does not get factored"; 
          return; 
        } 
 
        if( $a > 2000000000 ) {
          print "$a is too BIG, use a number less than two billion\n";
          return;
        }

my $count = 0; 
        my @factors = (); 
        my $min_i = 2; 
        my $work = ""; 
        while( $a > 1 ) { 
          my $imax = sqrt( $a )+1; 
          my $nothing_done = 1; 
          for( my $i = $min_i; $i < $imax && $i < $a; $i++) { 
            #print STDERR "i=$i, a=$a.\n"; 
            if( ($a % $i) == 0 ) { 
              push @factors, $i; 
               
              my $a1 = int( ($a+0.1)/$i ); 
 
              $work .= "$a is divisible by $i: $a = $a1 * $i.\n"; 
              $a = $a1; 
              $nothing_done = 0; 
              last; 
            } else { 
              $min_i = $i+1; 
            } 
          } 
           
          if( $nothing_done ) { 
            push @factors, $a; 
            last; 
          } 
           
        } 
 
        if( $a > 1 ) { 
          $work .= "$a is not divisible by anything.\n"; 
        } 
         
        if( $#factors > 0 ) { 
          print "$orig_a is NOT a prime number: $orig_a = " . join( " * ",@factors ) . "<BR>"; 
        } else { 
          print "$orig_a is a prime number\n"; 
        } 
        print "<H3>Work Shown</H3>\n<PRE>\n$work\n</PRE>"; 
        print 'This calculation used this <A HREF=Prime_factorization_algorithm.wikipedia>Prime Factorization Algorithm</A>.<BR>'; 
        $factors = join( ",", @factors );

==section output
factors

==section check
  a=6 factors=2,3