Integer factorization is crucial for modern cryptography, particularly because it underpins the security of widely used public key systems like RSA. An efficient integer factorization algorithm could compromise these systems, allowing for the rapid computation of the order of multiplicative groups and extending polynomial time algorithms from primes to composites. Beyond cryptography, such an algorithm could also enhance understanding of related problems, including the discrete logarithm problem and prime distribution. While no classical algorithm is known to efficiently factor integers, quantum computing offers potential solutions through Shor's algorithm. The reliance on the difficulty of factorization remains a cornerstone of cryptographic security today.