# Fundamental Theorems

## Fundamental Theorem Of Algebra, Fundamental Theorem Of CalculusFundamental theorem of arithmetic

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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