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• Fundamental_theorem_of_arithmetic abstract "In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors. For example,1200 = 24 × 31 × 52 = 3 × 2 × 2 × 2 × 2 × 5 × 5 = 5 × 2 × 3 × 2 × 5 × 2 × 2 = etc.The theorem is stating two things: first, that 1200 can be represented as a product of primes, and second, no matter how this is done, there will always be four 2s, one 3, two 5s, and no other primes in the product.The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (e.g. 12 = 2 × 6 = 3 × 4).This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, the factorization would not be unique, as, for example, 2 = 2×1 = 2×1×1 = ...".
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• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "Euclid's proof of the fundamental theorem of arithmetic".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "Fundamental theorem of arithmetic".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "Fundamental theorem of arithmetic#Canonical representation of a positive integer".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "Uniqueness of prime factorization".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "factorization into positive and negative prime powers".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "fundamental theorem of arithmetic".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "fundamental theorem".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "prime factorization".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "prime power decomposition".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "prime-power factorization".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "the fact".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "unique factorisation theorem".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "unique factorization into prime numbers".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "unique factorization theorem".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "unique factorization".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "unique prime factorization".
• Fundamental_theorem_of_arithmetic wikiPageWikiLinkText "uniqueness of prime factorizations".
• Fundamental_theorem_of_arithmetic title "Abnormal number".
• Fundamental_theorem_of_arithmetic title "Fundamental Theorem of Arithmetic".
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