The Fundamental Theorem

The Fundamental Theorem of Arithmetic says every integer greater than 1 has a single, unique prime factorization. Write 60 = 2² × 3 × 5, and no other combination of primes will ever multiply to 60. That uniqueness is what makes primes the mathematical equivalent of chemical elements: each number has exactly one recipe.

This single-recipe rule is quietly everywhere. It is why you can reduce a fraction to lowest terms, why a greatest common factor is well defined, and why RSA encryption works at all. Without unique factorization, arithmetic would lose the consistency we take for granted.