135199 ÷ 36 
We want to figure out the number of times 135199 can be divided by 36.

Going ahead to step 1:
If we divide 1 by 36, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 36

Advancing to step 2:
36 goes into 13 0 times with a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 36

On to step 3:
The number 36 fits into 135 3 times, leaving a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtract 108 from 135 to get 27.
Fetch the next digit (1) from the dividend, attach it to 27 and continue: 271 / 36

Advancing to step 4:
36 can be fit into 271 7 times, resulting in a remainder of 19.
Write down 7 as next digit of the result. 
Result so far: 37.0
If we subtract 252 from 271, we get 19.
Append the next digit (9) from the dividend to 19 and continue with: 199 / 36

Advancing to step 5:
199 divided by 36 is 5 with a remainder of 19.
Write down 5 as next digit of the result. 
Result so far: 375.0
If we take 180 away from 199, we end up with 19.
Bring next digit (9) of the dividend behind the 19 and repeat the process: 199 / 36

Step 6:
If we divide 199 by 36, we get 5 and a remainder of 19.
Record the quotient 5 as the next digit in the result. 
Result so far: 3755.0
Deduct 180 from 199 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 7:
36 goes into 190 5 times with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 3755.5
The remainder is 10 after subtracting 180 from 190.
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 8:
36 goes into 100 2 times with a remainder of 28.
Record the quotient 2 as the next digit in the result. 
Result so far: 3755.52
If we take 72 away from 100, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 9:
36 goes into 280 7 times with a remainder of 28.
The next digit of our result is 7. 
Result so far: 3755.527
The remainder is 28 after subtracting 252 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 10:
The number 36 fits into 280 7 times, leaving a remainder of 28.
The next digit of our result is 7. 
Result so far: 3755.5277
If we subtract 252 from 280, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The quotient of the division is 3755.5277, and the remainder is 0.00028.