663882 ÷ 44 
Our goal is to divide 663882 by 44.

Going ahead to step 1:
The number 44 fits into 6 0 times, leaving a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 44

Moving on to step 2:
The number 44 fits into 66 1 times, leaving a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 44 away from 66, we end up with 22.
Fetch the next digit (3) from the dividend, attach it to 22 and continue: 223 / 44

Let's proceed to step 3:
The number 44 fits into 223 5 times, leaving a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 15.0
Subtract 220 from 223 to get 3.
Include the next digit (8) from the dividend after 3, then repeat: 38 / 44

On to step 4:
When dividing 38 by 44, we get 0 with a remainder of 38.
Write down 0 as next digit of the result. 
Result so far: 150.0
If we subtract 0 from 38, we get 38.
Append the next digit (8) from the dividend to 38 and continue with: 388 / 44

On to step 5:
44 can be fit into 388 8 times, resulting in a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 1508.0
If we subtract 352 from 388, we get 36.
Append the next digit (2) from the dividend to 36 and continue with: 362 / 44

On to step 6:
362 divided by 44 is 8 with a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 15088.0
Subtract 352 from 362 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 7:
The number 44 fits into 100 2 times, leaving a remainder of 12.
The next digit of our result is 2. 
Result so far: 15088.2
If we subtract 88 from 100, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 8:
120 divided by 44 is 2 with a remainder of 32.
Write down 2 as next digit of the result. 
Result so far: 15088.22
Deduct 88 from 120 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 15088.22, and the remainder is 0.032.