To determine which of the given options is not a prime number, we will analyze each option step by step.
### Step-by-Step Solution:
1. **Understanding Prime Numbers**:
- A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. **Checking the Options**:
- We will check each option to see if it is a prime number or not.
3. **Option 1: 87**:
- Check if 87 is divisible by any number other than 1 and 87.
- The smallest prime number is 2. Since 87 is odd, it is not divisible by 2.
- Next, check divisibility by 3:
- Sum of digits of 87 = 8 + 7 = 15, which is divisible by 3.
- Therefore, 87 is divisible by 3 (87 = 3 × 29).
- Since 87 has divisors other than 1 and itself, **87 is not a prime number**.
4. **Option 2: 61**:
- Check if 61 is divisible by any prime numbers up to its square root (approximately 7.81).
- Check divisibility by 2, 3, 5, and 7:
- 61 is odd (not divisible by 2).
- Sum of digits = 6 + 1 = 7 (not divisible by 3).
- Last digit is not 0 or 5 (not divisible by 5).
- 61 divided by 7 is approximately 8.71 (not an integer).
- Since 61 has no divisors other than 1 and itself, **61 is a prime number**.
5. **Option 3: 79**:
- Similar to 61, check divisibility by prime numbers up to its square root (approximately 8.83).
- Check divisibility by 2, 3, 5, and 7:
- 79 is odd (not divisible by 2).
- Sum of digits = 7 + 9 = 16 (not divisible by 3).
- Last digit is not 0 or 5 (not divisible by 5).
- 79 divided by 7 is approximately 11.29 (not an integer).
- Since 79 has no divisors other than 1 and itself, **79 is a prime number**.
6. **Option 4: 89**:
- Check divisibility by prime numbers up to its square root (approximately 9.43).
- Check divisibility by 2, 3, 5, and 7:
- 89 is odd (not divisible by 2).
- Sum of digits = 8 + 9 = 17 (not divisible by 3).
- Last digit is not 0 or 5 (not divisible by 5).
- 89 divided by 7 is approximately 12.71 (not an integer).
- Since 89 has no divisors other than 1 and itself, **89 is a prime number**.
### Conclusion:
After checking all the options, we find that the only number that is not a prime number is **87**.
### Final Answer:
**87 is not a prime number.**
