We look at the division of 10869 by 13 
Our goal is to divide 10869 by 13.

Step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 13

Let's proceed to step 2:
13 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 13

On to step 3:
If we divide 108 by 13, we get 8 and a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we subtract 104 from 108, we get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 13

Moving on to step 4:
When dividing 46 by 13, we get 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 83.0
Subtracting 39 from 46 leaves us with 7.
Fetch the next digit (9) from the dividend, attach it to 7 and continue: 79 / 13

Step 5:
When dividing 79 by 13, we get 6 with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 836.0
Deduct 78 from 79 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.

On to step 6:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 836.0
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.

Going ahead to step 7:
13 goes into 100 7 times with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 836.07
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.

Let's proceed to 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: 836.076
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:
120 divided by 13 is 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 836.0769
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.

Advancing to step 10:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 836.07692
Subtracting 26 from 30 leaves us 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.

Let's proceed to step 11:
When dividing 40 by 13, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 836.076923
If we take 39 away from 40, 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.

Moving on 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: 836.076923
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.

Let's proceed to step 13:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 836.07692307
Subtracting 91 from 100 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.

The final result is 836.07692307 with a remainder of 9e-09.