defmodule CommonPrimeDivisors do
  def common_prime_divisors(a, b) do
    a
    |> Enum.zip(b)
    |> Enum.count(fn {x, y} ->
      d = gcd(x, y)
      remove_common(x, d) == 1 and remove_common(y, d) == 1
    end)
  end

  defp gcd(n, m) when rem(n, m) == 0, do: m
  defp gcd(n, m), do: gcd(m, rem(n, m))

  defp remove_common(1, _m), do: 1

  defp remove_common(n, m) do
    d = gcd(n, m)
    if d == 1, do: n, else: remove_common(div(n, d), m)
  end
end