We're dividing 135645 by 13 
Let's see how many times 13 fits into 135645.

Step 1:
13 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 13

On to step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 0 after subtracting 13 from 13.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 13

Going ahead to step 3:
When dividing 5 by 13, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Subtract 0 from 5 to get 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 13

Going ahead to step 4:
If we divide 56 by 13, we get 4 and a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 104.0
Deduct 52 from 56 and we're left with 4.
Grab the next digit (4) from the dividend, add it to 4, then carry on: 44 / 13

Step 5:
13 can be fit into 44 3 times, resulting in a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 1043.0
Subtracting 39 from 44 leaves us with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 13

Step 6:
The number 13 fits into 55 4 times, leaving a remainder of 3.
Put 4 as the next digit of the answer. 
Result so far: 10434.0
Deduct 52 from 55 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:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 10434.2
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.

Step 8:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 10434.23
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.

Let's proceed to step 9:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 10434.23
If we take 0 away from 10, we end up 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.

On to step 10:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 10434.2307
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.

Going ahead to step 11:
When dividing 90 by 13, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 10434.23076
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.

Going ahead to step 12:
If we divide 120 by 13, we get 9 and a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 10434.230769
The remainder is 3 after subtracting 117 from 120.
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 13:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 10434.2307692
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.

On to step 14:
If we divide 40 by 13, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 10434.23076923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 10434.23076923 with a balance of 1e-09.