Find which of the following numbers are primes :

Options

A. `87`
B. `89`
C. `63`
D. `91`

Answer

To determine which of the given numbers are prime, we will analyze each number based on the definition of prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Let's evaluate each number step by step:

### Step 1: Analyze the number 87
- **Divisors of 87**: 1, 3, 29, 87
- Since 87 has divisors other than 1 and itself (it is divisible by 3 and 29), it is **not a prime number**.

### Step 2: Analyze the number 89
- **Divisors of 89**: 1, 89
- Since 89 has no divisors other than 1 and itself, it is a **prime number**.

### Step 3: Analyze the number 63
- **Divisors of 63**: 1, 3, 7, 9, 21, 63
- Since 63 has divisors other than 1 and itself (it is divisible by 3, 7, 9, and 21), it is **not a prime number**.

### Step 4: Analyze the number 91
- **Divisors of 91**: 1, 7, 13, 91
- Since 91 has divisors other than 1 and itself (it is divisible by 7 and 13), it is **not a prime number**.

### Conclusion:
- The only prime number from the list is **89**.

### Summary of Results:
- 87: Not a prime number
- 89: Prime number
- 63: Not a prime number
- 91: Not a prime number

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