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Every positive integer can be written as the product of a sequence of prime numbers.

It can be proven that these sequences are unique: every integer can be written in one, and only one, way.
This is called the *fundamental theorem of arithmetic*.

For example, each prime number can only be written by multiplying itself by one, e.g. \(1 \times 7\).

The number 8 can be made by multiplying \(2 \times 2 \times 2\), but not by multiplying any other prime numbers.