12. State whether the number 97 is prime, composite, or neither.

Can you find any numbers other than 1 and 97 itself which divide evenly into 97 ?

If you cannot, then 97 is prime.

To determine whether the number 97 is prime, composite, or neither, we need to evaluate whether it has any factors other than 1 and itself.

In order to find the factors, we can divide 97 by all numbers from 2 up to the square root of 97, which is approximately 9.85. If any of these numbers divide 97 evenly (i.e., without a remainder), then 97 is not prime.

Let's go ahead and perform the calculation:
- Divide 97 by 2: 97 ÷ 2 = 48.5 (not evenly divisible)
- Divide 97 by 3: 97 ÷ 3 = 32.33 (not evenly divisible)
- Divide 97 by 4: 97 ÷ 4 = 24.25 (not evenly divisible)
- Divide 97 by 5: 97 ÷ 5 = 19.4 (not evenly divisible)
- Divide 97 by 6: 97 ÷ 6 = 16.17 (not evenly divisible)
- Divide 97 by 7: 97 ÷ 7 = 13.86 (not evenly divisible)
- Divide 97 by 8: 97 ÷ 8 = 12.13 (not evenly divisible)
- Divide 97 by 9: 97 ÷ 9 = 10.78 (not evenly divisible)

As we can see, there are no numbers from 2 to 9 that evenly divide 97. Therefore, 97 only has two factors: 1 and itself. This means that 97 is a prime number.

So, in conclusion, the number 97 is a prime number.