135564 ÷ 53 
Our goal is to divide 135564 by 53.

Advancing to step 1:
53 can be fit into 1 0 times, resulting in a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 53

On to step 2:
The number 53 fits into 13 0 times, leaving 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.
Bring next digit (5) of the dividend behind the 13 and repeat the process: 135 / 53

On to step 3:
53 goes into 135 2 times with a remainder of 29.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 106 from 135 and we're left with 29.
Take the next digit (5) from the dividend and append it to 29, then repeat: 295 / 53

Moving on to step 4:
When dividing 295 by 53, we get 5 with a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 25.0
If we take 265 away from 295, we end up with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 53

Advancing to step 5:
When dividing 306 by 53, we get 5 with a remainder of 41.
The next digit of our result is 5. 
Result so far: 255.0
If we subtract 265 from 306, we get 41.
Bring next digit (4) of the dividend behind the 41 and repeat the process: 414 / 53

Step 6:
414 divided by 53 is 7 with a remainder of 43.
Record the quotient 7 as the next digit in the result. 
Result so far: 2557.0
Deduct 371 from 414 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

On to step 7:
53 can be fit into 430 8 times, resulting in a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 2557.8
Subtract 424 from 430 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.

Moving on to step 8:
53 goes into 60 1 times with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 2557.81
If we take 53 away from 60, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
70 divided by 53 is 1 with a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 2557.811
The remainder is 17 after subtracting 53 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

The quotient of the division is 2557.811, and the remainder is 0.0017.