556779 ÷ 41 
Let's see how many times 41 fits into 556779.

Advancing to step 1:
41 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 41

Moving on to step 2:
41 goes into 55 1 times with a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 41 from 55 to get 14.
Include the next digit (6) from the dividend after 14, then repeat: 146 / 41

Step 3:
41 can be fit into 146 3 times, resulting in a remainder of 23.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Subtracting 123 from 146 leaves us with 23.
Append the next digit (7) from the dividend to 23 and continue with: 237 / 41

Advancing to step 4:
The number 41 fits into 237 5 times, leaving a remainder of 32.
The next digit of our result is 5. 
Result so far: 135.0
Subtracting 205 from 237 leaves us with 32.
Append the next digit (7) from the dividend to 32 and continue with: 327 / 41

Step 5:
41 goes into 327 7 times with a remainder of 40.
Put 7 as the next digit of the answer. 
Result so far: 1357.0
The remainder is 40 after subtracting 287 from 327.
Grab the next digit (9) from the dividend, add it to 40, then carry on: 409 / 41

Going ahead to step 6:
When dividing 409 by 41, we get 9 with a remainder of 40.
Put 9 as the next digit of the answer. 
Result so far: 13579.0
If we subtract 369 from 409, 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.

Let's proceed to step 7:
400 divided by 41 is 9 with a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 13579.9
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.

Going ahead to step 8:
41 can be fit into 310 7 times, resulting in a remainder of 23.
The next digit of our result is 7. 
Result so far: 13579.97
Subtract 287 from 310 to 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.

Moving on to step 9:
41 goes into 230 5 times with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 13579.975
Subtract 205 from 230 to 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 10:
When dividing 250 by 41, we get 6 with a remainder of 4.
The next digit of our result is 6. 
Result so far: 13579.9756
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.

Let's proceed to step 11:
41 goes into 40 0 times with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 13579.9756
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 12:
When dividing 400 by 41, we get 9 with a remainder of 31.
The next digit of our result is 9. 
Result so far: 13579.975609
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.

Let's proceed to step 13:
41 can be fit into 310 7 times, resulting in a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 13579.9756097
The remainder is 23 after subtracting 287 from 310.
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 14:
41 goes into 230 5 times with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 13579.97560975
The remainder is 25 after subtracting 205 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 13579.97560975 with a balance of 2.5e-08.