We're dividing 135965 by 52 
We're looking to find how many times 52 goes into 135965.

Going ahead to step 1:
If we divide 1 by 52, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 52

Moving on to step 2:
The number 52 fits into 13 0 times, leaving a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 13, we end up with 13.
Append the next digit (5) from the dividend to 13 and continue with: 135 / 52

On to step 3:
If we divide 135 by 52, we get 2 and a remainder of 31.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtracting 104 from 135 leaves us with 31.
Include the next digit (9) from the dividend after 31, then repeat: 319 / 52

Moving on to step 4:
52 can be fit into 319 6 times, resulting in a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
Deduct 312 from 319 and we're left with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 52

Moving on to step 5:
52 goes into 76 1 times with a remainder of 24.
The number 1 becomes the next digit in our result. 
Result so far: 261.0
Subtract 52 from 76 to get 24.
Fetch the next digit (5) from the dividend, attach it to 24 and continue: 245 / 52

Let's proceed to step 6:
52 goes into 245 4 times with a remainder of 37.
Put 4 as the next digit of the answer. 
Result so far: 2614.0
If we subtract 208 from 245, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

On to step 7:
370 divided by 52 is 7 with a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 2614.7
Subtracting 364 from 370 leaves us 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.

Going ahead to step 8:
When dividing 60 by 52, we get 1 with a remainder of 8.
The next digit of our result is 1. 
Result so far: 2614.71
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:
When dividing 80 by 52, we get 1 with a remainder of 28.
The number 1 becomes the next digit in our result. 
Result so far: 2614.711
Subtract 52 from 80 to 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.

Our division results in 2614.711 with a remaining 0.0028.