We look at the division of 725584 by 45 
We want to divide 725584 by 45.

Advancing to step 1:
The number 45 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (2) of the dividend behind the 7 and repeat the process: 72 / 45

On to step 2:
If we divide 72 by 45, we get 1 and a remainder of 27.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 45 from 72, we get 27.
Append the next digit (5) from the dividend to 27 and continue with: 275 / 45

Step 3:
45 goes into 275 6 times with a remainder of 5.
The next digit of our result is 6. 
Result so far: 16.0
Subtracting 270 from 275 leaves us with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 45

Step 4:
45 goes into 55 1 times with a remainder of 10.
Put 1 as the next digit of the answer. 
Result so far: 161.0
Subtract 45 from 55 to get 10.
Include the next digit (8) from the dividend after 10, then repeat: 108 / 45

Moving on to step 5:
108 divided by 45 is 2 with a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 1612.0
If we take 90 away from 108, we end up with 18.
Include the next digit (4) from the dividend after 18, then repeat: 184 / 45

Step 6:
45 goes into 184 4 times with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 16124.0
If we subtract 180 from 184, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 7:
If we divide 40 by 45, we get 0 and a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 16124.0
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 8:
When dividing 400 by 45, we get 8 with a remainder of 40.
Write down 8 as next digit of the result. 
Result so far: 16124.08
The remainder is 40 after subtracting 360 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 9:
45 can be fit into 400 8 times, resulting in a remainder of 40.
The number 8 becomes the next digit in our result. 
Result so far: 16124.088
Subtract 360 from 400 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Our division results in 16124.088 with a remaining 0.004.