To determine if 9 is a prime number or a composite number, we need to understand the definitions of both types of numbers.
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that it can only be divided evenly by 1 and the number itself. For example, the number 5 is prime because the only divisors are 1 and 5.
A composite number, on the other hand, is a natural number greater than 1 that has more than two positive divisors. This means it can be divided by numbers other than just 1 and itself. For instance, the number 6 is composite because it can be divided evenly by 1, 2, 3, and 6.
Now, let’s analyze the number 9. The positive divisors of 9 are 1, 3, and 9. Since 9 can be divided evenly by 3 (in addition to 1 and 9), it has more than two positive divisors. Therefore, we can conclude that:
- 9 is not a prime number because it can be divided by 3.
- 9 is a composite number because it has more than two divisors.
In summary, 9 is classified as a composite number.