The Fundamental Theorem of Arithmetic

Every composite number can be expressed as a product of primes in exactly one way (except for the order of factors). This uniqueness is what makes the theorem fundamental.

Think of prime factors as magnetic blocks that can only combine in one specific way. No matter how you rearrange them, they always form the same number.

The "Prince of Mathematics" (1777-1855) provided the first rigorous proof of this theorem in his masterwork "Disquisitiones Arithmeticae."

This uniqueness property is essential for number theory, cryptography, and ensures that prime factorization gives us the "DNA" of every number.