35565 ÷ 87 
Our goal is to divide 35565 by 87.

Going ahead to step 1:
If we divide 3 by 87, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 87

Step 2:
When dividing 35 by 87, we get 0 with a remainder of 35.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 35 and we're left with 35.
Append the next digit (5) from the dividend to 35 and continue with: 355 / 87

Going ahead to step 3:
87 can be fit into 355 4 times, resulting in a remainder of 7.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Deduct 348 from 355 and we're left with 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 87

Going ahead to step 4:
When dividing 76 by 87, we get 0 with a remainder of 76.
Use 0 as the next digit of our solution. 
Result so far: 40.0
If we take 0 away from 76, we end up with 76.
Fetch the next digit (5) from the dividend, attach it to 76 and continue: 765 / 87

Going ahead to step 5:
87 can be fit into 765 8 times, resulting in a remainder of 69.
Record the quotient 8 as the next digit in the result. 
Result so far: 408.0
Deduct 696 from 765 and we're left with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 6:
The number 87 fits into 690 7 times, leaving a remainder of 81.
Write down 7 as next digit of the result. 
Result so far: 408.7
If we take 609 away from 690, we end up with 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Advancing to step 7:
If we divide 810 by 87, we get 9 and a remainder of 27.
The next digit of our result is 9. 
Result so far: 408.79
Subtract 783 from 810 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 8:
270 divided by 87 is 3 with a remainder of 9.
The number 3 becomes the next digit in our result. 
Result so far: 408.793
Subtracting 261 from 270 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.

Moving on to step 9:
90 divided by 87 is 1 with a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 408.7931
Deduct 87 from 90 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.

Step 10:
87 can be fit into 30 0 times, resulting in a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 408.7931
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
300 divided by 87 is 3 with a remainder of 39.
The next digit of our result is 3. 
Result so far: 408.793103
Deduct 261 from 300 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Let's proceed to step 12:
390 divided by 87 is 4 with a remainder of 42.
Use 4 as the next digit of our solution. 
Result so far: 408.7931034
Subtract 348 from 390 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 13:
When dividing 420 by 87, we get 4 with a remainder of 72.
Write down 4 as next digit of the result. 
Result so far: 408.79310344
Subtracting 348 from 420 leaves us with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

The final result is 408.79310344 with a remainder of 7.2e-08.