Fundamental Theorem of Arithmetic

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 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not. For example,

1200 = 2^4 \times 3^1 \times 5^2 = 3 \times 2\times 2\times 2\times 2 \times 5 \times 5 = 5 \times 2\times 3\times 2\times 5 \times 2 \times 2 =\cdots\text { 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.

Read more about Fundamental Theorem Of Arithmetic:  History, Proof, Generalizations

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