Let's divide 565661 by 41
We're looking to find how many times 41 goes into 565661.

Step 1:
When dividing 5 by 41, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 41

Step 2:
41 goes into 56 1 times with a remainder of 15.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 41 away from 56, we end up with 15.
Take the next digit (5) from the dividend and append it to 15, then repeat: 155 / 41

Step 3:
When dividing 155 by 41, we get 3 with a remainder of 32.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 123 away from 155, we end up with 32.
Append the next digit (6) from the dividend to 32 and continue with: 326 / 41

Going ahead to step 4:
326 divided by 41 is 7 with a remainder of 39.
Record the quotient 7 as the next digit in the result. 
Result so far: 137.0
The remainder is 39 after subtracting 287 from 326.
Fetch the next digit (6) from the dividend, attach it to 39 and continue: 396 / 41

Moving on to step 5:
If we divide 396 by 41, we get 9 and a remainder of 27.
Record the quotient 9 as the next digit in the result. 
Result so far: 1379.0
The remainder is 27 after subtracting 369 from 396.
Append the next digit (1) from the dividend to 27 and continue with: 271 / 41

On to step 6:
The number 41 fits into 271 6 times, leaving a remainder of 25.
Put 6 as the next digit of the answer. 
Result so far: 13796.0
Subtracting 246 from 271 leaves us 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.

Advancing to step 7:
If we divide 250 by 41, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 13796.6
Deduct 246 from 250 and we're left 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.

On to step 8:
If we divide 40 by 41, we get 0 and a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 13796.6
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.

Step 9:
When dividing 400 by 41, we get 9 with a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 13796.609
If we take 369 away from 400, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Moving on to step 10:
When dividing 310 by 41, we get 7 with a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 13796.6097
If we subtract 287 from 310, we get 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 11:
If we divide 230 by 41, we get 5 and a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 13796.60975
If we take 205 away from 230, we end up 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.

Going ahead to step 12:
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: 13796.609756
If we subtract 246 from 250, we 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.

Advancing to step 13:
40 divided by 41 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 13796.609756
Deduct 0 from 40 and we're left 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.

Moving on to step 14:
41 can be fit into 400 9 times, resulting in a remainder of 31.
Record the quotient 9 as the next digit in the result. 
Result so far: 13796.60975609
Subtract 369 from 400 to 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.

After the division, we end up with 13796.60975609 and a remainder of 3.1e-08.