in reply to OT: Finding Factor Closest To Square Root

Doesn't use Math::Big::Factor, isn't particularly dynamic, doesn't have exponential complexity, and could be much faster in C. With all those caveats, here you go... 
#!/usr/bin/perl -w
use strict;

print sqrt_factor(shift), "\n";

sub sqrt_factor 
{
    my $n = shift;
    my $root = int(sqrt($n));

    for (my $i=$root; $i>1; $i--)
    {
        if( ($n % $i) == 0 )
        {   
            my $factor2 = int($n / $i);
            return (($root - $i)<($factor2 - $root)) ? $i : $factor2
        }
    }
    
    return 1;
}

[download]

-- All code is 100% tested and functional unless otherwise noted.

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Re^2: OT: Finding Factor Closest To Square Root
by QM (Parson) on Feb 20, 2005 at 07:20 UTC
    Yes, but this still takes a long time for large prime N, as it has to count down from sqrt(N) to 1.

    It would go twice as fast if we checked N%2==0. It would go six times as fast if we checked for N%3==0 also. Perhaps using GCD(N,sqrt(N)#) (where N# is the primorial of N) would improve the situation? The problem then becomes one of generating all primes upto sqrt(N), where we could cheat and just have a big list precomputed.

    ...Better yet, would a quick test of N for primality solve the problem of prime N?

    -QM
    --
    Quantum Mechanics: The dreams stuff is made of

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