1. **Problem:** Determine if the numbers 51, 87, and 59 are prime or not prime. 2. **Recall:** A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. 3. **Check 51:** - Test divisibility by small primes: 2 (no, since 51 is odd), 3 (yes, since $5+1=6$ which is divisible by 3). - Since 51 is divisible by 3, it is **not prime**. 4. **Check 87:** - Test divisibility by 2 (no, 87 is odd), 3 (yes, $8+7=15$ divisible by 3). - Since 87 is divisible by 3, it is **not prime**. 5. **Check 59:** - Test divisibility by primes less than $\sqrt{59} \approx 7.68$: 2 (no), 3 (no), 5 (no), 7 (no). - No divisors found, so 59 is **prime**. **Final answers:** - 51: Not prime - 87: Not prime - 59: Prime