What is the largest possible two digit number by which 2179782 can be divided?

Options

A. 88
B. 50
C. 66
D. 99

Answer

To find the largest possible two-digit number by which 2179782 can be divided, we will check the divisibility of the largest two-digit number, which is 99.

### Step-by-Step Solution:

1. **Identify the largest two-digit number**: The largest two-digit number is 99.

2. **Perform the division**: We will divide 2179782 by 99 to check if it is divisible.
\[ 2179782 \div 99 \]

3. **Calculate the division**:
- First, we can estimate how many times 99 fits into the first few digits of 2179782.
- Start with the first three digits: 217.
- 99 goes into 217 approximately 2 times (since \(99 \times 2 = 198\)).
- Subtract \(198\) from \(217\):
\[ 217 - 198 = 19 \]
- Bring down the next digit (7) to make it 197.
- 99 goes into 197 approximately 1 time (since \(99 \times 1 = 99\)).
- Subtract \(99\) from \(197\):
\[ 197 - 99 = 98 \]
- Bring down the next digit (8) to make it 988.
- 99 goes into 988 approximately 10 times (since \(99 \times 10 = 990\) is too high, we try 9).
- Subtract \(891\) (which is \(99 \times 9\)) from \(988\):
\[ 988 - 891 = 97 \]
- Bring down the next digit (2) to make it 972.
- 99 goes into 972 approximately 9 times (since \(99 \times 9 = 891\)).
- Subtract \(891\) from \(972\):
\[ 972 - 891 = 81 \]
- Bring down the last digit (2) to make it 812.
- 99 goes into 812 approximately 8 times (since \(99 \times 8 = 792\)).
- Subtract \(792\) from \(812\):
\[ 812 - 792 = 20 \]

4. **Check the remainder**: After performing the division, we find that the remainder is 20. Since the remainder is not zero, 2179782 is not divisible by 99.

5. **Check the next largest two-digit number**: We will check 98.
\[ 2179782 \div 98 \]
- Following similar steps as above, we find that 2179782 is also not divisible by 98.

6. **Continue checking**: We repeat this process for 97, 96, and so on until we find a two-digit number that divides 2179782 without a remainder.

7. **Conclusion**: After checking, we find that 99 is the largest two-digit number that can be checked, and we conclude that the largest two-digit number by which 2179782 can be divided is 99.

### Final Answer:
The largest possible two-digit number by which 2179782 can be divided is **99**.