The least number of 4 digits which is exactly divisible by 9 is

Options

A. 1018
B. 1026
C. 1009
D. 1008

Answer

To find the least number of 4 digits that is exactly divisible by 9, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the least 4-digit number**:
The smallest 4-digit number is 1000.

2. **Divide 1000 by 9**:
We need to check if 1000 is divisible by 9. To do this, we perform the division:
\[ 1000 \div 9 = 111 \quad \text{(quotient)} \]
The remainder can be calculated as:
\[ 1000 - (111 \times 9) = 1000 - 999 = 1 \]
So, the remainder is 1.

3. **Calculate the next number that is divisible by 9**:
Since 1000 gives a remainder of 1 when divided by 9, we need to add enough to reach the next multiple of 9. To find the next multiple of 9, we subtract the remainder from 9:
\[ 9 - 1 = 8 \]
Now, we add this to 1000:
\[ 1000 + 8 = 1008 \]

4. **Verify if 1008 is divisible by 9**:
To confirm that 1008 is divisible by 9, we can divide it:
\[ 1008 \div 9 = 112 \quad \text{(exactly)} \]
Since there is no remainder, 1008 is indeed divisible by 9.

### Final Answer:
The least number of 4 digits which is exactly divisible by 9 is **1008**.