To determine which of the given numbers has factors other than the number itself and one, we need to check their prime factorizations.
We are given five numbers to check: 97, 107, 167, 297, and 317.
A: 97
First, we see if 97 has any prime factors other than 1 and 97 itself.
97 is a prime number, meaning it has no factors other than 1 and itself.
B: 107
Next, we check 107 for any prime factors.
107 is also a prime number, meaning it has no factors other than 1 and itself.
C: 167
Now, we check 167 for prime factors.
167 is a prime number, meaning it has no factors other than 1 and itself.
D: 297
For 297, we need to check if it has any factors other than 1 and 297.
Upon factorization:
297 = 3^3 * 11^1
This means 297 can be divided by 3 and 11, which are factors other than 1 and itself. Therefore, 297 is not a prime number.
E: 317
Finally, we check 317 for prime factors.
317 is a prime number, meaning it has no factors other than 1 and itself.
From the above analysis:
- 97 is prime.
- 107 is prime.
- 167 is prime.
- 297 is not prime (it has factors 3 and 11).
- 317 is prime.
Therefore, the number that has factors other than itself and one is 297.
