Factor puzzles from definition to applications

Background: Factor puzzles are a salient tool that has been consigned to oblivion. Methods: In this paper, we introduce factor puzzles and study the existence and uniqueness of solutions along with their connections to other areas of mathematics and real-world applications. Results: Using concepts from elementary number theory, we prove several theorems pertinent to the existence and uniqueness of a solvable factor puzzle, and the number of solutions. Furthermore, we established connections between factor puzzles and polynomial as well as matrix factorizations. In addition, we demonstrate the importance of factor puzzles in the real world was evidenced by an application in cryptography. Conclusion: Factor puzzles are a prominent tool with many remarkable connections and real-world applications.