9. Determine whether or not the number 257 is prime.

257 is prime.

Step-by-step explanation:

To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.

In this case, √257 = 16.03 so we just need to see if 257 is divisible by 2, 3, 5, 7, 11 and 13 (the prime numbers that come before 16)

257 is odd, so it is not divisible by 2. The sum of its digits is 14, therefore, it is not divisible by 3. 257 ends in 7, therefore it's not divisible by 5. 257 / 7 = 36.71 so it's not divisible by 7. 257 / 11 = 23.36 so it's not divisible by 11 Finally 257 / 13 = 19.76 so it's not divisible by 13.

Therefore, 257 is prime.