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The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely as a product of primes. For the ring Z[√–5], although unique factorization holds for ideals, unique factorization fails for elements. We investigate both elements and ideals of Z[√–5]. For elements, we examine irreducibility (the analog of primality) in Z[√–5] and look at how often and how badly unique fac- torization fails. For ideals, we examine irreducibility again and a proof for unique factorization.