We're dividing 597166 by 11 
We're looking to find how many times 11 goes into 597166.

Step 1:
5 divided by 11 is 0 with 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.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 11

On to step 2:
The number 11 fits into 59 5 times, leaving a remainder of 4.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we subtract 55 from 59, we get 4.
Append the next digit (7) from the dividend to 4 and continue with: 47 / 11

Moving on to step 3:
47 divided by 11 is 4 with a remainder of 3.
Put 4 as the next digit of the answer. 
Result so far: 54.0
If we subtract 44 from 47, we get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 11

On to step 4:
31 divided by 11 is 2 with a remainder of 9.
Put 2 as the next digit of the answer. 
Result so far: 542.0
If we subtract 22 from 31, we get 9.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 11

Let's proceed to step 5:
11 can be fit into 96 8 times, resulting in a remainder of 8.
The next digit of our result is 8. 
Result so far: 5428.0
Subtract 88 from 96 to get 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 11

Moving on to step 6:
11 goes into 86 7 times with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 54287.0
Deduct 77 from 86 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.

Moving on to step 7:
90 divided by 11 is 8 with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 54287.8
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.

Let's proceed to step 8:
20 divided by 11 is 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 54287.81
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.

Going ahead to step 9:
11 can be fit into 90 8 times, resulting in a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 54287.818
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.

Let's proceed to step 10:
11 goes into 20 1 times with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 54287.8181
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 11:
If we divide 90 by 11, we get 8 and a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 54287.81818
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.

Advancing to step 12:
If we divide 20 by 11, we get 1 and a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 54287.818181
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.

Step 13:
90 divided by 11 is 8 with a remainder of 2.
The next digit of our result is 8. 
Result so far: 54287.8181818
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.

Let's proceed to step 14:
When dividing 20 by 11, we get 1 with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 54287.81818181
Subtract 11 from 20 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

After the division, we end up with 54287.81818181 and a remainder of 9e-09.