Why is the number 1 not composite or prime?

Answer 1

By definition, 1 is not prime. A Prime number has exactly two unique natural number divisors; itself and one. You can understand '1 and 1' to be two numbers, but they are not unique. The same reasoning brings us to the conclusion that 1 is not composite; a composite number can be divided without remainder by at least one integer other than itself and 1.

Answer 2

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.

Answer 3

A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.