We look at the division of 586631 by 11 
Our goal is to divide 586631 by 11.

Advancing to step 1:
The number 11 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 11

Going ahead to step 2:
11 can be fit into 58 5 times, resulting in a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Subtracting 55 from 58 leaves us with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 11

Advancing to step 3:
When dividing 36 by 11, we get 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 53.0
If we subtract 33 from 36, we get 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 11

Step 4:
The number 11 fits into 36 3 times, leaving a remainder of 3.
The next digit of our result is 3. 
Result so far: 533.0
Subtract 33 from 36 to get 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 11

Moving on to step 5:
If we divide 33 by 11, we get 3 and a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 5333.0
If we subtract 33 from 33, we get 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 11

Moving on to step 6:
1 divided by 11 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 53330.0
If we take 0 away from 1, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
11 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 53330.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
When dividing 100 by 11, we get 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 53330.09
If we take 99 away from 100, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 9:
If we divide 10 by 11, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 53330.09
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 10:
When dividing 100 by 11, we get 9 with a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 53330.0909
Subtracting 99 from 100 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 11:
If we divide 10 by 11, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 53330.0909
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 12:
When dividing 100 by 11, we get 9 with a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 53330.090909
If we subtract 99 from 100, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 13:
11 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 53330.090909
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 14:
11 can be fit into 100 9 times, resulting in a remainder of 1.
Write down 9 as next digit of the result. 
Result so far: 53330.09090909
The remainder is 1 after subtracting 99 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 53330.09090909 with a balance of 1e-09.