What is a key characteristic of prime numbers?

A key characteristic of prime numbers is that they can only be divided by themselves and 1 without leaving a remainder. This definition sets prime numbers apart from composite numbers, which are integers that have divisors other than one and themselves. For example, the number 7 is prime because its only divisors are 1 and 7, whereas 6 is composite because it can be divided evenly by 1, 2, 3, and 6. Understanding this characteristic helps in identifying and distinguishing prime numbers within the set of natural numbers.

The other options do not accurately describe prime numbers. For instance, not all prime numbers are even; in fact, the only even prime number is 2. Additionally, there isn’t a consistent relationship determining that prime numbers are always higher than all composite numbers, as some primes are smaller than composites. Finally, prime numbers cannot be divided by any integer; they only have two specific divisors, which reinforces their unique property.