What is the quotient when 777777 is divided by 11?

Options

A. 7007
B. 7070
C. 7707
D. 70707

Answer

To find the quotient when 777777 is divided by 11, we can follow these steps:

### Step 1: Set up the division
We want to divide 777777 by 11. We can write it as:
\[ 777777 \div 11 \]

### Step 2: Break down the number
Since 777777 consists of the digit '7' repeated six times, we can think of it as:
\[ 777777 = 7 \times 100000 + 7 \times 10000 + 7 \times 1000 + 7 \times 100 + 7 \times 10 + 7 \]

### Step 3: Perform the division
Now, we will divide 777777 by 11. We can do this step by step:

1. **Divide the first two digits (77) by 11:**
\[ 77 \div 11 = 7 \]
So, we write down 7 as the first digit of the quotient.

2. **Multiply 7 by 11:**
\[ 7 \times 11 = 77 \]
Subtract this from 77:
\[ 77 - 77 = 0 \]

3. **Bring down the next digit (7):**
Now we have 07 (or just 7).

4. **Divide 7 by 11:**
Since 7 is less than 11, we write down 0 in the quotient and bring down the next digit (7) to make it 77 again.

5. **Repeat the process:**
- Divide 77 by 11:
\[ 77 \div 11 = 7 \]
- Multiply and subtract:
\[ 77 - 77 = 0 \]
- Bring down the next digit (7) to make it 07 again, and repeat.

Continuing this process, we will find that we get 7 for each pair of 77 we divide.

### Step 4: Complete the division
After processing all the digits, we find that the quotient is:
\[ 70707 \]

### Final Answer
Thus, the quotient when 777777 is divided by 11 is:
\[ \boxed{70707} \]