The correct justification for whether 181 is prime or composite is:
B. 181 is prime because its only factors are 1 and itself.
To justify this: A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. To determine if 181 is prime, we check if it can be divided evenly by any integer other than 1 and itself.
When we check for factors, we find that 181 is not divisible by any prime numbers up to its square root (which is approximately 13.45). The prime numbers to check would be 2, 3, 5, 7, 11, and 13. Since 181 is not divisible by any of these, it has no divisors other than 1 and 181, thus confirming that it is indeed a prime number.
A, C, and D are incorrect because they incorrectly state that 181 has factors like 9 or 3, which it does not.