To determine whether a specific group of numbers consists entirely of prime numbers, we first need to know what a prime number is. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, it can only be divided evenly by 1 and the number itself.
Let’s consider a couple of examples of groups of numbers and evaluate whether they are all prime:
- Group A: 2, 3, 5, 7
- 2 is prime
- 3 is prime
- 5 is prime
- 7 is prime
- Group B: 4, 6, 9, 10
- 4 is not prime (divisible by 1, 2, 4)
- 6 is not prime (divisible by 1, 2, 3, 6)
- 9 is not prime (divisible by 1, 3, 9)
- 10 is not prime (divisible by 1, 2, 5, 10)
- Group C: 11, 13, 17, 19
- 11 is prime
- 13 is prime
- 17 is prime
- 19 is prime
In these examples, Group A and Group C consist entirely of prime numbers, whereas Group B does not. Therefore, if you are provided with a list of groups, you can evaluate them in a similar manner by checking the divisibility of each number in the group to confirm if they are all prime.