The Quadratic Sieve is a mathematical algorithm used for integer factorization, particularly effective for large numbers. It works by finding a set of numbers whose squares yield a specific congruence relation, allowing the algorithm to identify factors of the target number. This method is based on the principle of using quadratic residues and relies on a combination of linear algebra and number theory. The Quadratic Sieve is one of the fastest known factorization methods for numbers with around 100 digits, making it a valuable tool in fields like cryptography and computational mathematics.