function factorial_integer ($k)
{
  //variable and initializations
  $the_result = 1;

  //check to see if k is an integer
  if (!is_int($k))
  {
    return "error";
  }

  //check for k < 0
  if ($k < 0)
  {
    return "error";
  }

  //0! = 1
  if ($k == 0)
  {
    return 1;
  }

  //calculate the result
  for ($i = 2; $i <= $k; $i++)
  {
    $the_result = $the_result * $i;
  }

  //return the value
  return $the_result;
}