Integers are the whole numbers, negative whole numbers, and zero.
7 is odd since it's one more than 6, which is even. Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. See Notes and Literature on Prime Numbers from Understanding Mathematics by Peter Alfeld, and the Largest Known Primes page. Most mathematicians, at least when they're talking to each other, use Z to refer to the set of integers. In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.