We look at the division of 13765989 by 586 
We're looking to find how many times 586 goes into 13765989.

Advancing to step 1:
586 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 586

Let's proceed to step 2:
13 divided by 586 is 0 with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 586

Let's proceed to step 3:
586 can be fit into 137 0 times, resulting in a remainder of 137.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 137, we end up with 137.
Take the next digit (6) from the dividend and append it to 137, then repeat: 1376 / 586

On to step 4:
The number 586 fits into 1376 2 times, leaving a remainder of 204.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtract 1172 from 1376 to get 204.
Fetch the next digit (5) from the dividend, attach it to 204 and continue: 2045 / 586

Let's proceed to step 5:
2045 divided by 586 is 3 with a remainder of 287.
Record the quotient 3 as the next digit in the result. 
Result so far: 23.0
The remainder is 287 after subtracting 1758 from 2045.
Take the next digit (9) from the dividend and append it to 287, then repeat: 2879 / 586

Step 6:
2879 divided by 586 is 4 with a remainder of 535.
The number 4 becomes the next digit in our result. 
Result so far: 234.0
The remainder is 535 after subtracting 2344 from 2879.
Append the next digit (8) from the dividend to 535 and continue with: 5358 / 586

Let's proceed to step 7:
586 goes into 5358 9 times with a remainder of 84.
Record the quotient 9 as the next digit in the result. 
Result so far: 2349.0
If we subtract 5274 from 5358, we get 84.
Append the next digit (9) from the dividend to 84 and continue with: 849 / 586

Going ahead to step 8:
586 can be fit into 849 1 times, resulting in a remainder of 263.
Record the quotient 1 as the next digit in the result. 
Result so far: 23491.0
If we subtract 586 from 849, we get 263.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2630, and continue the process.

Let's proceed to step 9:
If we divide 2630 by 586, we get 4 and a remainder of 286.
The next digit of our result is 4. 
Result so far: 23491.4
Subtract 2344 from 2630 to get 286.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2860, and continue the process.

Let's proceed to step 10:
586 can be fit into 2860 4 times, resulting in a remainder of 516.
The next digit of our result is 4. 
Result so far: 23491.44
If we take 2344 away from 2860, we end up with 516.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5160, and continue the process.

Our division results in 23491.44 with a remaining 0.516.