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1 cannot be a composite number because it is not divisible by any number other than itself.


It is not a prime because of the fundamental theorem of arithmetic: the unique prime factorisation theorem. This states that any positive integer greater than 1 can be expressed as a product of a unique set of primes. If 1 were considered a prime then you could add any number of 1s to the set of factors and the product would not change. For example,12 = 2*2*3 or 1*2*2*3 or 1*1*1*1*2*2*3 : so that the factorisation is no longer unique.

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Q: Why is 1 not a prime or a composite?
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