No, two different prime numbers cannot divide each other.
A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. If one prime number were to divide another, it would mean that the second prime number is a multiple of the first. Since a prime number's only divisors are 1 and itself, the only way one prime number can divide another is if they are the same prime number.
For example:
- 7 is a prime number. Its only divisors are 1 and 7.
- 11 is a prime number. Its only divisors are 1 and 11.
7 cannot divide 11, and 11 cannot divide 7. The result of either division would be a non-integer number.
If we consider the question of whether a prime number can divide itself, then the answer is yes. For instance, 7 divides 7, because 7 / 7 = 1, which is an integer. However, the question usually implies two different prime numbers.
Therefore, distinct prime numbers cannot divide each other because of their fundamental property of having only 1 and themselves as divisors. If one prime divided another, it would contradict the definition of a prime number.
