Which of the following is a characteristic of prime numbers?

The characteristic that prime numbers can only be divided by one and themselves is fundamental to their definition. A prime number is defined as a natural number greater than one that has no positive divisors other than one and itself. This means that for prime numbers, the only factors are the number itself and the number one.

For example, the number 5 is a prime number because it can only be divided evenly (without leaving a remainder) by 1 and 5. In contrast, composite numbers have more than two divisors, which distinguishes them from prime numbers.

The other statements do not accurately reflect the definition of prime numbers. Some prime numbers are greater than 10, but not all of them are. For instance, the number 7 is a prime number but is not greater than 10. Additionally, while even numbers exist, the only even prime number is 2, as all other even numbers can be divided by 2, therefore having at least three divisors: one, themselves, and 2. Lastly, prime numbers can be quite varied and include several smaller numbers, so stating that they can only be divided by three numbers is incorrect, as that would imply they have additional factors.