How to get grandparent of a given category

You could write a simple function to do this each time you need to. Here’s an example I found on this website.

function pa_category_top_parent_id( $catid ) {
    while( $catid ) {
        $cat = get_category( $catid ); // get the object for the catid
        $catid = $cat->category_parent; // assign parent ID (if exists) to $catid
        // the while loop will continue whilst there is a $catid
        // when there is no longer a parent $catid will be NULL so we can assign our $catParent
        $catParent = $cat->cat_ID;
    }
    return $catParent;
}

Then you can use this function anywhere like so:

$catid = get_query_var( 'cat' );
echo pa_category_top_parent_id( $catid );

Reading the comments in the code it is pretty self-explanatory. Hope this helps.