We look at the division of 413900 by 71 
We want to figure out the number of times 413900 can be divided by 71.

Let's proceed to step 1:
71 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 71

On to step 2:
If we divide 41 by 71, we get 0 and a remainder of 41.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 41, we end up with 41.
Fetch the next digit (3) from the dividend, attach it to 41 and continue: 413 / 71

Let's proceed to step 3:
If we divide 413 by 71, we get 5 and a remainder of 58.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 355 from 413 and we're left with 58.
Bring next digit (9) of the dividend behind the 58 and repeat the process: 589 / 71

Step 4:
589 divided by 71 is 8 with a remainder of 21.
Record the quotient 8 as the next digit in the result. 
Result so far: 58.0
If we take 568 away from 589, we end up with 21.
Include the next digit (0) from the dividend after 21, then repeat: 210 / 71

Step 5:
If we divide 210 by 71, we get 2 and a remainder of 68.
Record the quotient 2 as the next digit in the result. 
Result so far: 582.0
If we subtract 142 from 210, we get 68.
Grab the next digit (0) from the dividend, add it to 68, then carry on: 680 / 71

Step 6:
71 can be fit into 680 9 times, resulting in a remainder of 41.
The next digit of our result is 9. 
Result so far: 5829.0
The remainder is 41 after subtracting 639 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

On to step 7:
71 can be fit into 410 5 times, resulting in a remainder of 55.
Write down 5 as next digit of the result. 
Result so far: 5829.5
Subtract 355 from 410 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 8:
When dividing 550 by 71, we get 7 with a remainder of 53.
The number 7 becomes the next digit in our result. 
Result so far: 5829.57
Subtracting 497 from 550 leaves us with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 9:
The number 71 fits into 530 7 times, leaving a remainder of 33.
The next digit of our result is 7. 
Result so far: 5829.577
Subtracting 497 from 530 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Our division results in 5829.577 with a remaining 0.0033.