577806 ÷ 11 
Let's see how many times 11 fits into 577806.

Step 1:
11 can be fit into 5 0 times, resulting in a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (7) from the dividend to 5 and continue with: 57 / 11

Moving on to step 2:
If we divide 57 by 11, we get 5 and a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtract 55 from 57 to get 2.
Grab the next digit (7) from the dividend, add it to 2, then carry on: 27 / 11

On to step 3:
When dividing 27 by 11, we get 2 with a remainder of 5.
The next digit of our result is 2. 
Result so far: 52.0
Subtract 22 from 27 to get 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 11

Let's proceed to step 4:
11 goes into 58 5 times with a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 525.0
If we subtract 55 from 58, we get 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 11

Going ahead to step 5:
11 can be fit into 30 2 times, resulting in a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 5252.0
Deduct 22 from 30 and we're left with 8.
Append the next digit (6) from the dividend to 8 and continue with: 86 / 11

Going ahead to step 6:
11 can be fit into 86 7 times, resulting in a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 52527.0
Subtracting 77 from 86 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
When dividing 90 by 11, we get 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 52527.8
Subtract 88 from 90 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 8:
If we divide 20 by 11, we get 1 and a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 52527.81
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
90 divided by 11 is 8 with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 52527.818
Subtracting 88 from 90 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 10:
20 divided by 11 is 1 with a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 52527.8181
The remainder is 9 after subtracting 11 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 11:
The number 11 fits into 90 8 times, leaving a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 52527.81818
Deduct 88 from 90 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 12:
The number 11 fits into 20 1 times, leaving a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 52527.818181
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 13:
11 goes into 90 8 times with a remainder of 2.
The next digit of our result is 8. 
Result so far: 52527.8181818
If we subtract 88 from 90, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 14:
If we divide 20 by 11, we get 1 and a remainder of 9.
The next digit of our result is 1. 
Result so far: 52527.81818181
Deduct 11 from 20 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

In conclusion, the division gives 52527.81818181 with a balance of 9e-09.