def get_power_and_remainder(n, p)
  q = 0
  while n % p == 0 do
    n /= p
    q += 1
  end

  [n, q]
end

def format_prime_factor(p, q)
  case q
  when 0
    ""
  when 1
    "(" + p.to_s + ")"
  else
    "(" + p.to_s + "**" + q.to_s + ")"
  end
end

def prime_factors(n)
  result = (2..Math.sqrt(n) + 1).reduce("") { |factors, p|
    n, q = get_power_and_remainder(n, p)
    factors + format_prime_factor(p, q)
  }

  if n > 1 then
    result += format_prime_factor(n, 1)
  end
  result
end