One can be divided by itself without a remainder. So can every positive whole number. That fact alone does not make a number prime. The key is how many distinct positive divisors it has.
Count different divisors
A prime number is a whole number greater than one with exactly two positive divisors: one and itself. For 7, those divisors are 1 and 7. For 2, they are 1 and 2. Both numbers meet the definition.
For 1, the divisor list contains only 1. Writing “one and itself” does not create two different entries, because both names refer to the same number. One therefore has a single positive divisor and is not prime. It is not composite either; composite numbers are greater than one and have more than two positive divisors.
Try a small sorting exercise
Write the numbers 1, 2, 4, 5 and 6 on separate cards. Beneath each, list every positive divisor. Sort the cards by the number of distinct entries rather than by whether the number is odd or even.
This reveals two useful points: 2 is prime even though it is even, and being odd is not sufficient for being prime. You can add 9 to the activity to test the second idea, since its divisors include 1, 3 and 9.
See why the definition is useful
Prime factorisation breaks a number greater than one into prime factors. For example, 12 = 2 × 2 × 3. If 1 were treated as a prime factor, you could keep adding extra factors of 1 without changing the product: 1 × 2 × 2 × 3, then 1 × 1 × 2 × 2 × 3, and so on.
Excluding 1 keeps the usual statement of unique prime factorisation clean. When explaining the idea to a learner, begin with the divisor count and use the factorisation example afterwards. It gives a reason the definition is useful without replacing the definition itself.