The expression of a positive integer as a product of prime numbers, which is unique for every integer greater than 1. This decomposition reveals the fundamental building blocks of the number.
From Latin 'primus' meaning 'first' and 'factoris' meaning 'maker' or 'doer.' The concept dates to ancient Greek mathematics, but the systematic study and terminology developed in the 18th and 19th centuries with advances in number theory.
Prime factorization is like finding the DNA of numbers - every integer has a unique genetic code made of primes! This uniqueness, guaranteed by the Fundamental Theorem of Arithmetic, makes prime factorization the backbone of modern cryptography and computer security.
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