Tuberculosis (TB) is an infectious disease caused by the bacterium Mycobacterium tuberculosis and primarily affects the lungs, as well as other body parts. TB is spread through the air when an infected person coughs, sneezes, or talks. Medical doctors diagnose TB in patients via clinical examinations and specialized tests. However, coughing is a common symptom of respiratory diseases such as TB. Literature suggests that cough sounds coming from different respiratory diseases can be distinguished by both medical doctors and computer algorithms. Therefore, cough recordings associated with patients with and without TB seems to be a reasonable avenue of investigation. In this work, we utilize a very large dataset of TB and non-TB cough audio recordings obtained from the south-east of Africa, India, and the south-east of Asia using a fully automated phone-based application (Hyfe), without manual annotation. We fit statistical classifiers based on spectral and time domain features with and without clinical metadata. A stratified grouped cross-validation approach shows that an average Area Under Curve (AUC) of approximately 0.70 $\pm$ 0.05 both for a cough-level and a participant-level classification can be achieved using cough sounds alone. The addition of demographic and clinical factors increases performance, resulting in an average AUC of approximately 0.81 $\pm$ 0.05. Our results suggest mobile phone-based applications that integrate clinical symptoms and cough sound analysis could help community health workers and, most importantly, health service programs to improve TB case-finding efforts while reducing costs, which could substantially improve public health.