We look at the division of 561959 by 41 
We want to figure out the number of times 561959 can be divided by 41.

Going ahead to step 1:
41 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 41

Advancing to step 2:
41 can be fit into 56 1 times, resulting in a remainder of 15.
The next digit of our result is 1. 
Result so far: 1.0
If we take 41 away from 56, we end up with 15.
Take the next digit (1) from the dividend and append it to 15, then repeat: 151 / 41

Advancing to step 3:
41 goes into 151 3 times with a remainder of 28.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Deduct 123 from 151 and we're left with 28.
Take the next digit (9) from the dividend and append it to 28, then repeat: 289 / 41

Going ahead to step 4:
41 goes into 289 7 times with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 137.0
If we take 287 away from 289, we end up with 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 41

Step 5:
The number 41 fits into 25 0 times, leaving a remainder of 25.
Put 0 as the next digit of the answer. 
Result so far: 1370.0
Deduct 0 from 25 and we're left with 25.
Bring next digit (9) of the dividend behind the 25 and repeat the process: 259 / 41

Step 6:
The number 41 fits into 259 6 times, leaving a remainder of 13.
Write down 6 as next digit of the result. 
Result so far: 13706.0
Subtract 246 from 259 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
130 divided by 41 is 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 13706.3
Subtracting 123 from 130 leaves us 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 8:
The number 41 fits into 70 1 times, leaving a remainder of 29.
The next digit of our result is 1. 
Result so far: 13706.31
The remainder is 29 after subtracting 41 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

On to step 9:
41 can be fit into 290 7 times, resulting in a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 13706.317
Subtracting 287 from 290 leaves us 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.

Advancing to step 10:
When dividing 30 by 41, we get 0 with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 13706.317
If we take 0 away from 30, we end up with 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 41 is 7 with a remainder of 13.
The next digit of our result is 7. 
Result so far: 13706.31707
Subtracting 287 from 300 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 12:
If we divide 130 by 41, we get 3 and a remainder of 7.
The next digit of our result is 3. 
Result so far: 13706.317073
Deduct 123 from 130 and we're left 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.

Advancing to step 13:
If we divide 70 by 41, we get 1 and a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 13706.3170731
Subtract 41 from 70 to get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 14:
The number 41 fits into 290 7 times, leaving a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 13706.31707317
Subtract 287 from 290 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 13706.31707317 and a remainder of 3e-09.