Which of the following number is divisible by 999?

Options

A. (A) 9999999
B. (B) 99999
C. (C) 987654321
D. (D) 145854

Answer

To determine which of the given numbers is divisible by 999, we can follow these steps:

### Step 1: Factor 999
First, we can factor 999 to understand its divisibility conditions:
\[ 999 = 9 \times 111 = 9 \times 3 \times 37 \]
This means that any number divisible by 999 must also be divisible by both 9 and 37.

### Step 2: Check divisibility by 9
To check if a number is divisible by 9, we need to find the sum of its digits. If the sum is divisible by 9, then the number itself is divisible by 9.

### Step 3: Check divisibility by 37
After confirming that a number is divisible by 9, we then need to check if it is divisible by 37. This can be done through long division or other methods.

### Step 4: Apply the checks to the options
Now, we will apply these checks to each option provided.

#### Option A: Check the first number
1. Calculate the sum of the digits.
2. Check if the sum is divisible by 9.
3. If it is, check divisibility by 37.

#### Option B: Check the second number
1. Calculate the sum of the digits.
2. Check if the sum is divisible by 9.
3. If it is, check divisibility by 37.

#### Option C: Check the third number
1. Calculate the sum of the digits.
2. Check if the sum is divisible by 9.
3. If it is, check divisibility by 37.

#### Option D: Check the fourth number
1. Calculate the sum of the digits.
2. Check if the sum is divisible by 9.
3. If it is, check divisibility by 37.

### Step 5: Conclusion
After checking all options, we will conclude which number is divisible by 999.

### Example Calculation for Option D (145854):
1. **Sum of digits**:
\[ 1 + 4 + 5 + 8 + 5 + 4 = 27 \]
Since \(27\) is divisible by \(9\), we proceed to check divisibility by \(37\).

2. **Check divisibility by 37**:
- We can use long division or a calculator to determine if \(145854\) is divisible by \(37\).
- Dividing \(145854\) by \(37\) gives \(3940\), which is a whole number.

Since \(145854\) is divisible by both \(9\) and \(37\), it is also divisible by \(999\).

### Final Answer:
The number that is divisible by 999 is **145854**.

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