605634 ÷ 41 
Our goal is to divide 605634 by 41.

On to step 1:
If we divide 6 by 41, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (0) from the dividend and append it to 6, then repeat: 60 / 41

On to step 2:
60 divided by 41 is 1 with a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 41 from 60 to get 19.
Bring next digit (5) of the dividend behind the 19 and repeat the process: 195 / 41

Moving on to step 3:
If we divide 195 by 41, we get 4 and a remainder of 31.
Write down 4 as next digit of the result. 
Result so far: 14.0
If we subtract 164 from 195, we get 31.
Grab the next digit (6) from the dividend, add it to 31, then carry on: 316 / 41

On to step 4:
41 can be fit into 316 7 times, resulting in a remainder of 29.
Put 7 as the next digit of the answer. 
Result so far: 147.0
Subtract 287 from 316 to get 29.
Bring next digit (3) of the dividend behind the 29 and repeat the process: 293 / 41

Advancing to step 5:
When dividing 293 by 41, we get 7 with a remainder of 6.
The next digit of our result is 7. 
Result so far: 1477.0
The remainder is 6 after subtracting 287 from 293.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 41

On to step 6:
If we divide 64 by 41, we get 1 and a remainder of 23.
Put 1 as the next digit of the answer. 
Result so far: 14771.0
Subtracting 41 from 64 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
41 goes into 230 5 times with a remainder of 25.
The next digit of our result is 5. 
Result so far: 14771.5
Deduct 205 from 230 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
When dividing 250 by 41, we get 6 with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 14771.56
Subtract 246 from 250 to get 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 9:
41 can be fit into 40 0 times, resulting in a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 14771.56
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 10:
If we divide 400 by 41, we get 9 and a remainder of 31.
Write down 9 as next digit of the result. 
Result so far: 14771.5609
If we subtract 369 from 400, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 11:
41 goes into 310 7 times with a remainder of 23.
Record the quotient 7 as the next digit in the result. 
Result so far: 14771.56097
If we take 287 away from 310, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 12:
41 can be fit into 230 5 times, resulting in a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 14771.560975
If we subtract 205 from 230, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 13:
41 goes into 250 6 times with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 14771.5609756
If we take 246 away from 250, we end up 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.

Moving on to step 14:
41 can be fit into 40 0 times, resulting in a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 14771.5609756
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The final result is 14771.5609756 with a remainder of 4e-08.