We look at the division of 66723 by 45 
Our goal is to divide 66723 by 45.

Let's proceed to step 1:
The number 45 fits into 6 0 times, leaving a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 45

Step 2:
If we divide 66 by 45, we get 1 and a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 45 from 66 to get 21.
Take the next digit (7) from the dividend and append it to 21, then repeat: 217 / 45

Moving on to step 3:
The number 45 fits into 217 4 times, leaving a remainder of 37.
The number 4 becomes the next digit in our result. 
Result so far: 14.0
Subtract 180 from 217 to get 37.
Fetch the next digit (2) from the dividend, attach it to 37 and continue: 372 / 45

On to step 4:
372 divided by 45 is 8 with a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 148.0
Deduct 360 from 372 and we're left with 12.
Append the next digit (3) from the dividend to 12 and continue with: 123 / 45

Moving on to step 5:
45 goes into 123 2 times with a remainder of 33.
Write down 2 as next digit of the result. 
Result so far: 1482.0
Deduct 90 from 123 and we're left 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.

Moving on to step 6:
330 divided by 45 is 7 with a remainder of 15.
Put 7 as the next digit of the answer. 
Result so far: 1482.7
Subtract 315 from 330 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
If we divide 150 by 45, we get 3 and a remainder of 15.
Put 3 as the next digit of the answer. 
Result so far: 1482.73
Subtract 135 from 150 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 8:
150 divided by 45 is 3 with a remainder of 15.
Use 3 as the next digit of our solution. 
Result so far: 1482.733
If we subtract 135 from 150, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The final result is 1482.733 with a remainder of 0.0015.