Finding the Largest Prime Factor of a Composite Number

gistfile1.rb

def maxPrimeFactor(n) #=> maxPrimeFactor(600851475143) => 6857 in 2007.562 ms
  # limit the ridiculous range safely
  range = n**(1/Math.sqrt(n.to_s.length).floor.to_f)
  ary = (1..range).to_a
  # Sieve of Eratosthenes (replace with Sieve of Atkin?)
  for i in ary
    for j in ary
      if i != j
        if (j % i == 0)
          ary.delete(j)
        end
      end
    end
  end
  #remove non-factor primes
  ary.delete_if{|k| ( n % k != 0)}
  ary.max
end