Which of the following is correct about 9999 ?

Options

A. It is a prime number
B. It Is an even number
C. It is divisible by 11
D. It is divisible by 6

Answer

To determine which statements about the number 9999 are correct, we will analyze its properties step by step.

### Step 1: Check if 9999 is a Prime Number
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The only divisors of a prime number are 1 and itself.

- **Calculation**: We can check if 9999 is divisible by any prime number. Let's start with 11.

\[ 9999 \div 11 = 909 \]

Since 9999 is divisible by 11 (it gives a whole number), it cannot be a prime number.

### Step 2: Check if 9999 is an Even Number
An even number is any integer that is exactly divisible by 2.

- **Calculation**: We divide 9999 by 2.

\[ 9999 \div 2 = 4999.5 \]

Since the result is not a whole number, 9999 is not an even number.

### Step 3: Check if 9999 is Divisible by 11
We already found in Step 1 that 9999 is divisible by 11.

- **Conclusion**:

\[ 9999 \div 11 = 909 \]

This confirms that 9999 is divisible by 11.

### Step 4: Check if 9999 is Divisible by 6
A number is divisible by 6 if it is divisible by both 2 and 3. We already established that 9999 is not divisible by 2.

- **Calculation for Divisibility by 3**: We can check if the sum of the digits of 9999 is divisible by 3.

\[ 9 + 9 + 9 + 9 = 36 \]

Since 36 is divisible by 3, 9999 is divisible by 3, but since it is not divisible by 2, it is not divisible by 6.

### Conclusion
Based on the analysis:
- 9999 is **not a prime number**.
- 9999 is **not an even number**.
- 9999 **is divisible by 11**.
- 9999 **is not divisible by 6**.

Thus, the correct statement about 9999 is that it is divisible by 11.