This function will build and return an array of all parent category id's that an article belongs to.

getCategories.php

/**
 * This function will build and return an array of all parent category id's that an article belongs to.
 * Written by René Kreijveld, email [at] renekreijveld.nl
 * 22-feb-2017
 *
 * Example function call for an article with id = 100:
 * $parentCategories = $this->getCategories(100, 0);
 *
 */
private function getCategories($artId, $catId)
{
	$db = JFactory::getDBO();
	// $catId = 0, so search the category of the article with id $artId.
	if ($catId == 0)
	{
		$query = $db->getQuery(true)
			->select($db->quoteName('catid'))
			->from($db->quoteName('#__content'))
			->where($db->quoteName('id') . ' = ' . (int) $artId);
		$db->setQuery($query);
		$parent = $db->loadResult();
		$this->categories[] = $parent;
		$this->getCategories(0, $parent);
	}
	// $artId = 0, so search the parent category of the category with id $catId.
	if ($artId == 0)
	{
		$query = $db->getQuery(true)
			->select($db->quoteName('parent_id'))
			->from($db->quoteName('#__categories'))
			->where($db->quoteName('id') . ' = ' . (int) $catId);
		$db->setQuery($query);
		$parent = $db->loadResult();
		if ($parent != 1)
		{
			$this->categories[] = $parent;
			$this->getCategories(0, $parent);
		}
	}
	return $this->categories;
}