583590 ÷ 71 
We want to divide 583590 by 71.

Step 1:
71 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 71

Step 2:
The number 71 fits into 58 0 times, leaving a remainder of 58.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 58 and we're left with 58.
Take the next digit (3) from the dividend and append it to 58, then repeat: 583 / 71

On to step 3:
71 goes into 583 8 times with a remainder of 15.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtract 568 from 583 to get 15.
Append the next digit (5) from the dividend to 15 and continue with: 155 / 71

Let's proceed to step 4:
The number 71 fits into 155 2 times, leaving a remainder of 13.
The number 2 becomes the next digit in our result. 
Result so far: 82.0
If we take 142 away from 155, we end up with 13.
Take the next digit (9) from the dividend and append it to 13, then repeat: 139 / 71

Going ahead to step 5:
If we divide 139 by 71, we get 1 and a remainder of 68.
The next digit of our result is 1. 
Result so far: 821.0
The remainder is 68 after subtracting 71 from 139.
Grab the next digit (0) from the dividend, add it to 68, then carry on: 680 / 71

Step 6:
If we divide 680 by 71, we get 9 and a remainder of 41.
Record the quotient 9 as the next digit in the result. 
Result so far: 8219.0
Subtract 639 from 680 to get 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Step 7:
When dividing 410 by 71, we get 5 with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 8219.5
If we subtract 355 from 410, we 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.

Moving on to step 8:
550 divided by 71 is 7 with a remainder of 53.
Use 7 as the next digit of our solution. 
Result so far: 8219.57
If we take 497 away from 550, we end up 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.

Moving on to step 9:
530 divided by 71 is 7 with a remainder of 33.
Record the quotient 7 as the next digit in the result. 
Result so far: 8219.577
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.

The final outcome is 8219.577, with a leftover of 0.0033.