The largest number of `6` digits which is exactly divisible by `6` is

Options

A. `999980`
B. `999982`
C. `999984`
D. `999964`

Answer

To find the largest six-digit number that is exactly divisible by 6, we can follow these steps:

### Step 1: Identify the largest six-digit number
The largest six-digit number is 999999.

### Step 2: Check divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3.

1. **Divisibility by 2**: A number is divisible by 2 if its last digit is even.
2. **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3.

### Step 3: Check if 999999 is divisible by 2
The last digit of 999999 is 9, which is odd. Therefore, 999999 is not divisible by 2.

### Step 4: Find the largest even six-digit number
Since 999999 is not divisible by 2, we need to check the next largest even number, which is 999998.

### Step 5: Check if 999998 is divisible by 3
Calculate the sum of the digits of 999998:
- 9 + 9 + 9 + 9 + 9 + 8 = 53

Now, check if 53 is divisible by 3:
- 53 ÷ 3 = 17 remainder 2 (not divisible by 3)

### Step 6: Check the next even number, 999996
Now, we check 999996:
- The last digit is 6 (even), so it is divisible by 2.
- Calculate the sum of the digits: 9 + 9 + 9 + 9 + 9 + 6 = 51

Now, check if 51 is divisible by 3:
- 51 ÷ 3 = 17 (divisible by 3)

### Conclusion
Since 999996 is divisible by both 2 and 3, it is divisible by 6. Therefore, the largest six-digit number that is exactly divisible by 6 is **999996**.