1. **Determine whether the number 57 is prime or composite.** A prime number has exactly two distinct positive divisors: 1 and itself. A composite number has more than two positive divisors. 2. **Check divisibility of 57:** - 57 is divisible by 3 because $5 + 7 = 12$ and 12 is divisible by 3. - Therefore, 57 has divisors 1, 3, 19, and 57. 3. **Conclusion:** - Since 57 has divisors other than 1 and itself, it is **composite**. --- 1. **Determine whether the number 59 is prime or composite.** 2. **Check divisibility of 59:** - Check divisibility by primes less than $\sqrt{59} \approx 7.68$: 2, 3, 5, 7. - 59 is not even, so not divisible by 2. - Sum of digits is 14, not divisible by 3. - Last digit is not 0 or 5, so not divisible by 5. - 59 divided by 7 is not an integer. 3. **Conclusion:** - 59 has no divisors other than 1 and itself, so it is **prime**. --- 1. **Determine whether the number 197 is prime or composite.** 2. **Check divisibility of 197:** - Check primes less than $\sqrt{197} \approx 14.04$: 2, 3, 5, 7, 11, 13. - 197 is not even. - Sum of digits is 17, not divisible by 3. - Last digit not 0 or 5. - 197 divided by 7, 11, or 13 is not an integer. 3. **Conclusion:** - 197 has no divisors other than 1 and itself, so it is **prime**.