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Any Positive Integer can be represented in exactly one way as a Product of Primes. The theorem is also called the Unique Factorization Theorem. The fundamental theorem of arithmetic is a Corollary of the first of Euclid's Theorems (Hardy and Wright 1979).
See also Euclid's Theorems, Integer, Prime Number
References
Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.
Oxford, England: Oxford University Press, p. 23, 1996.
Hardy, G. H. and Wright, E. M. ``Statement of the Fundamental Theorem of Arithmetic,'' ``Proof of the Fundamental Theorem of
Arithmetic,'' and ``Another Proof of the Fundamental Theorem of Arithmetic.'' §1.3, 2.10 and 2.11 in
An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 3 and 21, 1979.