634771 ÷ 71 
Our goal is to divide 634771 by 71.

Moving on to step 1:
When dividing 6 by 71, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 71

Advancing to step 2:
If we divide 63 by 71, we get 0 and a remainder of 63.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 63 and we're left with 63.
Include the next digit (4) from the dividend after 63, then repeat: 634 / 71

Let's proceed to step 3:
634 divided by 71 is 8 with a remainder of 66.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtracting 568 from 634 leaves us with 66.
Append the next digit (7) from the dividend to 66 and continue with: 667 / 71

Moving on to step 4:
667 divided by 71 is 9 with a remainder of 28.
The next digit of our result is 9. 
Result so far: 89.0
If we subtract 639 from 667, we get 28.
Bring next digit (7) of the dividend behind the 28 and repeat the process: 287 / 71

Moving on to step 5:
If we divide 287 by 71, we get 4 and a remainder of 3.
Put 4 as the next digit of the answer. 
Result so far: 894.0
Subtract 284 from 287 to get 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 71

On to step 6:
If we divide 31 by 71, we get 0 and a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 8940.0
Subtract 0 from 31 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.

Advancing to step 7:
If we divide 310 by 71, we get 4 and a remainder of 26.
The number 4 becomes the next digit in our result. 
Result so far: 8940.4
Deduct 284 from 310 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 8:
If we divide 260 by 71, we get 3 and a remainder of 47.
Put 3 as the next digit of the answer. 
Result so far: 8940.43
Subtract 213 from 260 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Advancing to step 9:
71 goes into 470 6 times with a remainder of 44.
The number 6 becomes the next digit in our result. 
Result so far: 8940.436
The remainder is 44 after subtracting 426 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 10:
When dividing 440 by 71, we get 6 with a remainder of 14.
Use 6 as the next digit of our solution. 
Result so far: 8940.4366
Subtract 426 from 440 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Our division results in 8940.4366 with a remaining 0.00014.