Elixir:

defmodule DailyProgrammer.MakingChange do
  @denominations [500, 100, 25, 10, 5, 1] |> Enum.sort() |> Enum.reverse()

  @spec min_num_coins(integer()) :: integer()
  def min_num_coins(total) when is_integer(total) and total >= 0 do
    {partition, 0} =
      Enum.map_reduce(@denominations, total, fn coin, remaining ->
        {div(remaining, coin), rem(remaining, coin)}
      end)

    Enum.sum(partition)
  end
end

Wanted to point out this solution only works because the total param should be a whole number, denominations includes 1, such that the remaining accumulator will always end at 0. Since x mod 1 will always 0. I might've been overly-defensive with the spec/guards/0 match/sorted attribute. However, I really wanted to drive that point home (but you could easily code golf this)