See by product id if product in category, if so which ones. Else not in any.

prodsareincat.php

<?php
require '../app/Mage.php';
umask(0);
Mage::app('admin');
 
error_reporting(1);
set_time_limit(0);
ini_set('memory_limit', '2048M');
 

 $productId = 11569;
$product = Mage::getModel('catalog/product')->load($productId);

$cats = $product->getCategoryIds();
foreach ($cats as $category_id) {
    $_cat = Mage::getModel('catalog/category')->load($category_id) ;
    if($_cat->getName()){
	     echo $category_id." => ".$_cat->getName()."</br>";
    } else{
	    echo "not in";
    }
   
    
} 
?>