We look at the division of 584535 by 45 
Our goal is to divide 584535 by 45.

Let's proceed to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 45

Moving on to step 2:
If we divide 58 by 45, we get 1 and a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 45 from 58 leaves us with 13.
Grab the next digit (4) from the dividend, add it to 13, then carry on: 134 / 45

Going ahead to step 3:
If we divide 134 by 45, we get 2 and a remainder of 44.
Use 2 as the next digit of our solution. 
Result so far: 12.0
The remainder is 44 after subtracting 90 from 134.
Bring next digit (5) of the dividend behind the 44 and repeat the process: 445 / 45

On to step 4:
If we divide 445 by 45, we get 9 and a remainder of 40.
The next digit of our result is 9. 
Result so far: 129.0
The remainder is 40 after subtracting 405 from 445.
Append the next digit (3) from the dividend to 40 and continue with: 403 / 45

On to step 5:
403 divided by 45 is 8 with a remainder of 43.
Record the quotient 8 as the next digit in the result. 
Result so far: 1298.0
If we take 360 away from 403, we end up with 43.
Grab the next digit (5) from the dividend, add it to 43, then carry on: 435 / 45

Advancing to step 6:
The number 45 fits into 435 9 times, leaving a remainder of 30.
Write down 9 as next digit of the result. 
Result so far: 12989.0
If we take 405 away from 435, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 7:
If we divide 300 by 45, we get 6 and a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 12989.6
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 8:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 12989.66
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 12989.66 with a remainder of 0.03.