Challenges in composite number factorization are critical to the fields of information systems security and cryptography. This study meticulously examined the features of triangular numbers and systematically created a Factoring Table for both triangular and non-triangular numbers, enabling the factorization of any composite number.  In turn, the study presents a novel number factorization algorithm, derived from this table and articulated through both a formula and instructions. Furthermore, the demonstration of primality testing was revealed to differentiate it from composite numbers. The specified algorithm can enhance the knowledge and security of key generation for the Rivest-Shamir-Adleman (RSA) system.