We're dividing 135107 by 13 
We want to figure out the number of times 135107 can be divided by 13.

On to step 1:
13 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 13

Going ahead to step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 13 from 13 and we're left with 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 13

Let's proceed to step 3:
The number 13 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 10.0
Subtracting 0 from 5 leaves us with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 13

Let's proceed to step 4:
The number 13 fits into 51 3 times, leaving a remainder of 12.
Use 3 as the next digit of our solution. 
Result so far: 103.0
Deduct 39 from 51 and we're left with 12.
Include the next digit (0) from the dividend after 12, then repeat: 120 / 13

Advancing to step 5:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 1039.0
Deduct 117 from 120 and we're left with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 13

On to step 6:
13 goes into 37 2 times with a remainder of 11.
The next digit of our result is 2. 
Result so far: 10392.0
The remainder is 11 after subtracting 26 from 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 7:
If we divide 110 by 13, we get 8 and a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 10392.8
Subtract 104 from 110 to 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.

Advancing to step 8:
13 goes into 60 4 times with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 10392.84
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.

Step 9:
80 divided by 13 is 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 10392.846
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.

Advancing to step 10:
13 goes into 20 1 times with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 10392.8461
If we subtract 13 from 20, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
13 goes into 70 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 10392.84615
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.

Advancing to step 12:
If we divide 50 by 13, we get 3 and a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 10392.846153
Deduct 39 from 50 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 13:
13 goes into 110 8 times with a remainder of 6.
The next digit of our result is 8. 
Result so far: 10392.8461538
If we take 104 away from 110, we end up 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.

Moving on to step 14:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The next digit of our result is 4. 
Result so far: 10392.84615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

In conclusion, the division gives 10392.84615384 with a balance of 8e-09.