Which number should be added to 459045 to make it exactly divisible by 27?

Options

A. 3
B. 9
C. 0
D. None of these

Answer

To find the number that should be added to 459045 to make it exactly divisible by 27, we can follow these steps:

### Step 1: Divide 459045 by 27
First, we need to perform the division of 459045 by 27 to find the remainder.

\[ 459045 \div 27 \]

### Step 2: Calculate the Quotient and Remainder
Perform the division:

1. 27 goes into 45 one time (1 × 27 = 27), leaving a remainder of 18 (45 - 27).
2. Bring down the next digit (9), making it 189.
3. 27 goes into 189 seven times (7 × 27 = 189), leaving a remainder of 0.
4. Bring down the next digit (0), making it 0.
5. Bring down the next digit (4), making it 4.
6. 27 goes into 4 zero times (0 × 27 = 0), leaving a remainder of 4.
7. Bring down the next digit (5), making it 45.
8. 27 goes into 45 one time (1 × 27 = 27), leaving a remainder of 18.

So, the complete calculation gives us:

\[ 459045 \div 27 = 17038 \quad \text{with a remainder of } 18. \]

### Step 3: Determine the Number to Add
To make 459045 exactly divisible by 27, we need to eliminate the remainder. Since the remainder is 18, we need to add enough to reach the next multiple of 27.

The next multiple of 27 after 459045 can be found by adding:

\[ 27 - \text{remainder} = 27 - 18 = 9. \]

### Step 4: Conclusion
Thus, the number that should be added to 459045 to make it exactly divisible by 27 is:

\[ \boxed{9}. \]