Which of the given numbers has factors other than the number itself and one?

A. 97
B. [tex]107[/tex]
C. 167
D. [tex]297[/tex]
E. [tex]317[/tex]



Answer :

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.