We look at the division of 580206 by 13 
We're looking to find how many times 13 goes into 580206.

Advancing to step 1:
When dividing 5 by 13, we get 0 with 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.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 13

Advancing to step 2:
When dividing 58 by 13, we get 4 with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Subtract 52 from 58 to get 6.
Append the next digit (0) from the dividend to 6 and continue with: 60 / 13

Let's proceed to step 3:
60 divided by 13 is 4 with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 44.0
Deduct 52 from 60 and we're left with 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 13

Let's proceed to step 4:
13 can be fit into 82 6 times, resulting in a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 446.0
Deduct 78 from 82 and we're left with 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 13

Step 5:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 4463.0
Subtracting 39 from 40 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 13

Moving on to step 6:
The number 13 fits into 16 1 times, leaving a remainder of 3.
The next digit of our result is 1. 
Result so far: 44631.0
Deduct 13 from 16 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 44631.2
Deduct 26 from 30 and we're left with 4.
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 8:
13 goes into 40 3 times with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 44631.23
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 9:
When dividing 10 by 13, we get 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 44631.23
Subtract 0 from 10 to 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 10:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 44631.2307
If we take 91 away from 100, we end up 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.

Advancing to step 11:
When dividing 90 by 13, we get 6 with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 44631.23076
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.

Advancing to step 12:
120 divided by 13 is 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 44631.230769
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 13:
30 divided by 13 is 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 44631.2307692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 14:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 44631.23076923
Deduct 39 from 40 and we're left 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.

The final result is 44631.23076923 with a remainder of 1e-09.