Question

Zero is neither a prime nor a composite number.Why?

Answer 1

The fundamental theory of arithmetic states that any number can be expressed as the product of two prime numbers. If 0 was a prime number, it wouldn't work because any number multiplied by 0 would equal 0, which gives it more than 2 factors. If it was considered composite, it can't be expressed as a product of 2 primes because in order for the product to equal 0, you would have to multiply by 0, which we've assumed to be composite.

For an integer to be prime it must be greater than 1, and the only integers that divide into it exactly are 1 and itself such as 3 and 13, etc. 0 is less than 1 so can't be prime. Composite integers are those that are the products of primes such as 6 = 2x3. 0 cannot be expressed as a product of primes because such products are non-zero.