FizzBuzz without modulo or division

fizzbuzz.rb

class FizzBuzz
  def run
    (1..100).each do |number|
      result = ''
      if divisible_by_3?(number)
        result << "Fizz"
      end

      if divisible_by_5?(number)
        result << "Buzz"
      end

      if result == ''
        result = number.to_s
      end
      puts result
    end
  end

  def divisible_by_3?(number)
    digits = number.to_s.split('')
    while digits.length > 1 do
      digits = digits.map(&:to_i).reduce(:+).to_s.split('')
    end
    [3,6,9].include?(digits.first.to_i)
  end

  def divisible_by_5?(number)
    last_digit = number.to_s[-1].to_i
    [0,5].include?(last_digit)
  end
end

FizzBuzz.new.run