109258 ÷ 13 
Our goal is to divide 109258 by 13.

Advancing to step 1:
When dividing 1 by 13, we get 0 with 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.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

Let's proceed to step 2:
When dividing 10 by 13, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 13

Going ahead to step 3:
The number 13 fits into 109 8 times, leaving a remainder of 5.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
The remainder is 5 after subtracting 104 from 109.
Take the next digit (2) from the dividend and append it to 5, then repeat: 52 / 13

Moving on to step 4:
When dividing 52 by 13, we get 4 with a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 84.0
If we subtract 52 from 52, we get 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 13

On to step 5:
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: 840.0
Subtract 0 from 5 to get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 13

Advancing to step 6:
13 can be fit into 58 4 times, resulting in a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 8404.0
Deduct 52 from 58 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 8404.4
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 8:
When dividing 80 by 13, we get 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 8404.46
Subtract 78 from 80 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.

Step 9:
13 goes into 20 1 times with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 8404.461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 10:
If we divide 70 by 13, we get 5 and a remainder of 5.
The next digit of our result is 5. 
Result so far: 8404.4615
Deduct 65 from 70 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 11:
50 divided by 13 is 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 8404.46153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 12:
When dividing 110 by 13, we get 8 with a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 8404.461538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 13:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 8404.4615384
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 14:
When dividing 80 by 13, we get 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 8404.46153846
If we subtract 78 from 80, 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.

The final result is 8404.46153846 with a remainder of 2e-09.