Fundamental Theorem of Arithmetic

Math for CS · Axiom Academy

Fundamental Theorem of Arithmetic The building blocks of all integers This is one of the most important theorems in all of mathematics. It states something profound: every integer greater than 1 can be expressed as a product of primes in exactly one way. Examples of Prime Factorization = product of common primes with minimum exponents = product of all primes with maximum exponents Algorithm: Finding Prime Factorization Every integer > 1 has a unique prime factorization Primes are the "atoms" of integer arithmetic This uniqueness enables GCD/LCM computation and divisibility testing Cryptography relies on the hardness of factoring large numbers The theorem is a cornerstone of modern number theory and computer science

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