We're dividing 580639 by 71 
Our goal is to divide 580639 by 71.

Let's proceed to step 1:
The number 71 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 71

Step 2:
If we divide 58 by 71, we get 0 and a remainder of 58.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 58 to get 58.
Take the next digit (0) from the dividend and append it to 58, then repeat: 580 / 71

Moving on to step 3:
If we divide 580 by 71, we get 8 and a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtract 568 from 580 to get 12.
Grab the next digit (6) from the dividend, add it to 12, then carry on: 126 / 71

Moving on to step 4:
126 divided by 71 is 1 with a remainder of 55.
Use 1 as the next digit of our solution. 
Result so far: 81.0
If we take 71 away from 126, we end up with 55.
Append the next digit (3) from the dividend to 55 and continue with: 553 / 71

Moving on to step 5:
The number 71 fits into 553 7 times, leaving a remainder of 56.
Use 7 as the next digit of our solution. 
Result so far: 817.0
Subtract 497 from 553 to get 56.
Append the next digit (9) from the dividend to 56 and continue with: 569 / 71

Let's proceed to step 6:
When dividing 569 by 71, we get 8 with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 8178.0
Subtracting 568 from 569 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
When dividing 10 by 71, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 8178.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
If we divide 100 by 71, we get 1 and a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 8178.01
If we subtract 71 from 100, we 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.

Advancing to step 9:
When dividing 290 by 71, we get 4 with a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 8178.014
If we take 284 away from 290, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 10:
71 goes into 60 0 times with a remainder of 60.
Record the quotient 0 as the next digit in the result. 
Result so far: 8178.014
Deduct 0 from 60 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 11:
If we divide 600 by 71, we get 8 and a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 8178.01408
If we take 568 away from 600, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 12:
If we divide 320 by 71, we get 4 and a remainder of 36.
Write down 4 as next digit of the result. 
Result so far: 8178.014084
If we take 284 away from 320, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 13:
71 can be fit into 360 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 8178.0140845
If we take 355 away from 360, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 14:
71 goes into 50 0 times with a remainder of 50.
The next digit of our result is 0. 
Result so far: 8178.0140845
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final outcome is 8178.0140845, with a leftover of 5e-08.