They are neither
Both zero and one are considered neither prime nor composite.
Zero and one.
First, zero is not applied to the terms prime and composite because the definitions only apply to natural numbers (positive whole numbers, which does not include zero). One is not prime or composite because one is the unit that is used within the definition of prime of composite numbers, and many definitions of prime and composite even exclude one from the definition. If you want to categorize one within a discussion of prime and composite, it is common to simply call one the unit.
Zero is neither composite nor prime.
Zero and one are neither prime nor composite, every other positive integer is one or the other.
It is 1 that is not considered to be a prime or a composite number because it has only one factor which is itself
There is no name for numbers which are neither prime nor composite.
One and zero, respectively.
Neither.
One is neither a prime nor a composite number. A prime number is one with exactly two positive divisors, itself and one. One has only one positive divisor which is itself so it is not prime. Furthermore, it cannot be written as a product of two factors, neither of which is itself. This tells us that one is also not composite. The other number which is neither prime not composite is Zero which has an infinite number of divisors since any nonzero whole number divides zero. Zero cannot be be written as a product of two factors, neither of which is itself, so zero is also not composite.
One is neither a prime nor a composite number. A prime number is one with exactly two positive divisors, itself and one. One has only one positive divisor which is itself so it is not prime. Furthermore, it cannot be written as a product of two factors, neither of which is itself. This tells us that one is also not composite. The other number which is neither prime not composite is Zero which has an infinite number of divisors since any nonzero whole number divides zero. Zero cannot be be written as a product of two factors, neither of which is itself, so zero is also not composite.
Zero is an even number but it is not composite (nor prime).