Nine is not a prime number. It is a composite number, because it has more than two factors. A prime number is only divisible by one and by itself, and nine is divisible by one and by nine, but it is also divisible by the number three.
One way of understanding the difference between prime numbers and composite numbers is to visualize a rectangle of a given area. Since the area of a rectangle is found by multiplying length times width, the length and width can be understood as the possible factors of the area. If the area is a prime number, there can be only one set of whole number dimensions possible. For example, a rectangle with an area of seven must have sides of one and seven. If the area is a composite number, then there can be numerous solutions. For example, if the area is nine, then the rectangle could have sides of one and nine or three and three.