Custom post type is seen as 'standard'

I use the fallowing piece of code in my index.php:

<?php get_template_part('content', get_post_format()); ?>

I have a custom post type called ‘quote’ who has it’s own 2 pages:
content-quote.php
and
single-quote.php

The problem now is that the get_post_format() returns ‘false’ wish means ‘standard’. I expect it to be ‘quote’. Why is this happening?

I have changed the main loop with the fallowing code to add ‘quote’ type:

if (!function_exists('wpf_main_query')) {
	function wpf_main_query($query) {
		if (is_home() and $query->is_main_query() or is_feed())
			$query->set('post_type', array('post', 'quote'));

		return $query;
	}
}
add_filter('pre_get_posts', 'wpf_main_query');

I got a second question:
Do I need to add this:

add_theme_support('post-formats', array('quote'));

When I use the register_post_type() to register my ‘quote’-posttype?