We're dividing 580651 by 90 
We want to figure out the number of times 580651 can be divided by 90.

On to step 1:
If we divide 5 by 90, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 90

On to step 2:
If we divide 58 by 90, we get 0 and a remainder of 58.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 58 after subtracting 0 from 58.
Fetch the next digit (0) from the dividend, attach it to 58 and continue: 580 / 90

Moving on to step 3:
90 goes into 580 6 times with a remainder of 40.
Write down 6 as next digit of the result. 
Result so far: 6.0
Deduct 540 from 580 and we're left with 40.
Grab the next digit (6) from the dividend, add it to 40, then carry on: 406 / 90

Going ahead to step 4:
When dividing 406 by 90, we get 4 with a remainder of 46.
The next digit of our result is 4. 
Result so far: 64.0
The remainder is 46 after subtracting 360 from 406.
Append the next digit (5) from the dividend to 46 and continue with: 465 / 90

On to step 5:
90 goes into 465 5 times with a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 645.0
Subtracting 450 from 465 leaves us with 15.
Take the next digit (1) from the dividend and append it to 15, then repeat: 151 / 90

Going ahead to step 6:
151 divided by 90 is 1 with a remainder of 61.
Use 1 as the next digit of our solution. 
Result so far: 6451.0
If we take 90 away from 151, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Moving on to step 7:
90 can be fit into 610 6 times, resulting in a remainder of 70.
The next digit of our result is 6. 
Result so far: 6451.6
Deduct 540 from 610 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 8:
When dividing 700 by 90, we get 7 with a remainder of 70.
Write down 7 as next digit of the result. 
Result so far: 6451.67
The remainder is 70 after subtracting 630 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 9:
When dividing 700 by 90, we get 7 with a remainder of 70.
Put 7 as the next digit of the answer. 
Result so far: 6451.677
Subtract 630 from 700 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

The final result is 6451.677 with a remainder of 0.007.