Project Euler #003 solution, comparing with square root

euler_003.rb

require 'benchmark'

the_number = 600_851_475_143

# monkeypatching
class Fixnum
  def prime? # O(n)
    (2..(self - 1)).each do |divisor|
      return false if self % divisor == 0
    end
    true
  end

  def prime_sqrt? # O(n)
    (2..Math.sqrt(self).to_i).each do |divisor|
      return false if self % divisor == 0
    end
    true
  end

  def factors
    result = self
    divisors = [] # O(n)
    (1..self).each do |divisor|
      break if result == 1
      if result % divisor == 0
        result /= divisor
        divisors << divisor
      end
    end
    divisors
  end

  def factors_sqrt
    result = self
    divisors = [] # O(n)
    (1..Math.sqrt(self)).each do |divisor|
      break if result == 1
      if result % divisor == 0
        result /= divisor
        divisors << divisor
      end
    end
    divisors
  end

  def prime_factors
    factors.select { |number| number.prime? }
  end

  def prime_factors_sqrt
    factors_sqrt.select { |number| number.prime? }
  end

end

time = Benchmark.realtime do
  the_number.prime_factors.last
end
puts "Original:\t#{time*1000} milliseconds"

time_sqrt = Benchmark.realtime do
  the_number.prime_factors_sqrt.last
end

puts "Math.sqrt:\t#{time_sqrt*1000} milliseconds"