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Fundamental Theorems - Fundamental Theorem Of Algebra, Fundamental Theorem Of Calculus - Fundamental theorem of arithmetic

branch subject prime

A fundamental theorem is a statement or proposition so named because it has consequences for the subject matter that are difficult to overestimate. Put another way, a fundamental theorem lies at the very heart of the subject. Mathematicians have designated one theorem in each main branch as fundamental to that branch.


The fundamental theorem of arithmetic states that every number can be written as the product of prime numbers in essentially one way. For example, there are no prime factors of 30 other than 2, 3, and 5. You cannot factor 30 so that it contains 2s and a 7 or some other combination.


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