Fundamental theorem of arithmetic

In mathematics, and in particular number theory, the fundamental theorem of arithmetic or unique factorization theorem is the statement that every positive integer greater than 1 is either a prime number or can be written as a product of prime numbers. Furthermore this factorization is unique except for the order. For instance, we can write

Related Topics:
Mathematics - Number theory - Integer - Prime number

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:6936 = 23 · 3 · 172   or   1200 = 24 · 3 · 52

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and there are no other possible factorizations of 6936 or 1200 into prime numbers, if we ignore the ordering of the factors.

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To make the theorem work even for the number 1, we can think of 1 as being the product of zero prime numbers (see empty product).

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