To determine if any of the numbers from 97 to 100 are prime, we need to evaluate each number individually. Let's go through the process step-by-step:
1. Checking if 97 is prime:
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- To check if 97 is prime, we test divisibility by all numbers from 2 up to [tex]\(\sqrt{97}\)[/tex], which is approximately 9.8. Therefore, we need to check divisibility by 2, 3, 4, 5, 6, 7, 8, and 9.
- 97 is not divisible by 2 (it is odd).
- 97 is not divisible by 3 (the sum of its digits, 9+7=16, is not divisible by 3).
- 97 is not divisible by 4 (it doesn't end in 0, 4, or 8, and 97/4 is not a whole number).
- 97 is not divisible by 5 (it does not end in 0 or 5).
- 97 is not divisible by 6 (not divisible by 2 or 3).
- 97 is not divisible by 7 (97 / 7 is not a whole number).
- 97 is not divisible by 8 (97 / 8 is not a whole number).
- 97 is not divisible by 9 (not a whole number when divided by 9).
- Since 97 is not divisible by any of these numbers, it is indeed a prime number.
2. Additional checks (for completeness):
- Even though we find that 97 is prime, let’s briefly verify the primality of 98, 99, and 100.
- 98: Divisible by 2 (it is even), so not prime.
- 99: Divisible by 3 (the sum of its digits, 9+9=18, is divisible by 3), so not prime.
- 100: Divisible by 2 and 5 (it ends in 0), so not prime.
Since 97 is a prime number, we do not need to factor or check any numbers lower than 97.
Conclusion:
Among the numbers 97 to 100, the prime number is 97. Hence, the answer to the question is 97.
