As the popularity of Android smart phones has increased in recent years, so too has the number of malicious applications. Due to the potential for data theft mobile phone users face, the detection of malware on Android devices has become an increasingly important issue in cyber security. Traditional methods like signature-based routines are unable to protect users from the ever-increasing sophistication and rapid behavior changes in new types of Android malware. Therefore, a great deal of effort has been made recently to use machine learning models and methods to characterize and generalize the malicious behavior patterns of mobile apps for malware detection. In this paper, we propose a novel and highly reliable classifier for Android Malware detection based on a Factorization Machine architecture and the extraction of Android app features from manifest files and source code. Our results indicate that the numerical feature representation of an app typically results in a long and highly sparse vector and that the interactions among different features are critical to revealing malicious behavior patterns. After performing an extensive performance evaluation, our proposed method achieved a test result of 100.00% precision score on the DREBIN dataset and 99.22% precision score with only 1.10% false positive rate on the AMD dataset. These metrics match the performance of state-of-the-art machine-learning-based Android malware detection methods and several commercial antivirus engines with the benefit of training up to 50 times faster.