We look at the division of 5646 by 72 
Our goal is to divide 5646 by 72.

Step 1:
The number 72 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 72

Let's proceed to step 2:
72 can be fit into 56 0 times, resulting in a remainder of 56.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 56 leaves us with 56.
Grab the next digit (4) from the dividend, add it to 56, then carry on: 564 / 72

Step 3:
The number 72 fits into 564 7 times, leaving a remainder of 60.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 504 from 564 leaves us with 60.
Take the next digit (6) from the dividend and append it to 60, then repeat: 606 / 72

On to step 4:
If we divide 606 by 72, we get 8 and a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 78.0
Deduct 576 from 606 and we're left 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.

Moving on to step 5:
72 can be fit into 300 4 times, resulting in a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 78.4
Deduct 288 from 300 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 6:
The number 72 fits into 120 1 times, leaving a remainder of 48.
Write down 1 as next digit of the result. 
Result so far: 78.41
Subtracting 72 from 120 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 7:
480 divided by 72 is 6 with a remainder of 48.
The number 6 becomes the next digit in our result. 
Result so far: 78.416
If we subtract 432 from 480, we get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 8:
72 can be fit into 480 6 times, resulting in a remainder of 48.
The next digit of our result is 6. 
Result so far: 78.4166
Deduct 432 from 480 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

The final result is 78.4166 with a remainder of 0.00048.