We divide 580100 by 90
Our goal is to divide 580100 by 90.

Step 1:
90 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 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.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 58 leaves us with 58.
Take the next digit (0) from the dividend and append it to 58, then repeat: 580 / 90

Step 3:
If we divide 580 by 90, we get 6 and a remainder of 40.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 540 away from 580, we end up with 40.
Take the next digit (1) from the dividend and append it to 40, then repeat: 401 / 90

Step 4:
90 can be fit into 401 4 times, resulting in a remainder of 41.
The next digit of our result is 4. 
Result so far: 64.0
Subtract 360 from 401 to get 41.
Include the next digit (0) from the dividend after 41, then repeat: 410 / 90

Going ahead to step 5:
If we divide 410 by 90, we get 4 and a remainder of 50.
The number 4 becomes the next digit in our result. 
Result so far: 644.0
If we subtract 360 from 410, we get 50.
Fetch the next digit (0) from the dividend, attach it to 50 and continue: 500 / 90

Step 6:
If we divide 500 by 90, we get 5 and a remainder of 50.
The next digit of our result is 5. 
Result so far: 6445.0
If we take 450 away from 500, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 7:
The number 90 fits into 500 5 times, leaving a remainder of 50.
The number 5 becomes the next digit in our result. 
Result so far: 6445.5
If we subtract 450 from 500, we 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.

On to step 8:
When dividing 500 by 90, we get 5 with a remainder of 50.
Put 5 as the next digit of the answer. 
Result so far: 6445.55
Subtracting 450 from 500 leaves us with 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 quotient of the division is 6445.55, and the remainder is 0.05.