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0 and 1
This question is about "which number neither prime nor composite"
A number is called prime number which have two positive divisors, one and itself. 1 has only one positive divistor that is itself. therefore 1 is not a prime number.
1 cannot be written as a product of two factors, so 1 is also not composite. 1 is also have a unique property that 1 is a number whose reciprocal is also itself which is also a whole number. Anyway 1 is neither prime nor composite number.
Any non zero whole number can divide zero. So zero has infinite number of divisors. For checking prime number we need a number which have two positive divisors, one and itself. So Zero is not a prime number.
Zero can not written as product of two factor, so zero is also not composite. Zero has also a unique property that when it multiplied by some number, their prodcut again give the result zero.
Therefore 1 and 0 both are neither prime nor composite number.