1 is neither prime nor a composite number because it only has 1 divisor, 1 and 1, and it doesn't have more than 2 integral divisors, like stated, it only has 1. So it falls in neither category.
A prime number has exactly two integral divisors: 1 and itself. Because it contains only one divisor, the number 1 is not a prime. A whole number with more than two integral divisors is called a composite number. So, with the exception of 0 and 1, all whole integers are either prime or composite.
