We look at the division of 598166 by 13 
We're looking to find how many times 13 goes into 598166.

Advancing to step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 13

Advancing to step 2:
13 can be fit into 59 4 times, resulting in a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtract 52 from 59 to get 7.
Grab the next digit (8) from the dividend, add it to 7, then carry on: 78 / 13

Moving on to step 3:
The number 13 fits into 78 6 times, leaving a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 46.0
Deduct 78 from 78 and we're left with 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 13

Going ahead to step 4:
When dividing 1 by 13, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 460.0
Subtract 0 from 1 to get 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 13

Going ahead to step 5:
The number 13 fits into 16 1 times, leaving a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 4601.0
The remainder is 3 after subtracting 13 from 16.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 13

Let's proceed to step 6:
If we divide 36 by 13, we get 2 and a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 46012.0
Deduct 26 from 36 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.

On to step 7:
100 divided by 13 is 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 46012.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 8:
If we divide 90 by 13, we get 6 and a remainder of 12.
The next digit of our result is 6. 
Result so far: 46012.76
If we subtract 78 from 90, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 46012.769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 10:
If we divide 30 by 13, we get 2 and a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 46012.7692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 11:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 46012.76923
The remainder is 1 after subtracting 39 from 40.
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 12:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 46012.76923
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.

Advancing to step 13:
13 goes into 100 7 times with a remainder of 9.
The next digit of our result is 7. 
Result so far: 46012.7692307
If we subtract 91 from 100, we 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.

Step 14:
When dividing 90 by 13, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 46012.76923076
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 46012.76923076 with a balance of 1.2e-08.