105544 ÷ 44 
We want to figure out the number of times 105544 can be divided by 44.

Advancing to step 1:
1 divided by 44 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 44

Going ahead to step 2:
44 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 44

Going ahead to step 3:
When dividing 105 by 44, we get 2 with a remainder of 17.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 88 from 105 and we're left with 17.
Fetch the next digit (5) from the dividend, attach it to 17 and continue: 175 / 44

Moving on to step 4:
If we divide 175 by 44, we get 3 and a remainder of 43.
The number 3 becomes the next digit in our result. 
Result so far: 23.0
If we take 132 away from 175, we end up with 43.
Append the next digit (4) from the dividend to 43 and continue with: 434 / 44

Let's proceed to step 5:
When dividing 434 by 44, we get 9 with a remainder of 38.
Record the quotient 9 as the next digit in the result. 
Result so far: 239.0
If we subtract 396 from 434, we get 38.
Bring next digit (4) of the dividend behind the 38 and repeat the process: 384 / 44

Going ahead to step 6:
44 can be fit into 384 8 times, resulting in a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 2398.0
If we take 352 away from 384, we end up 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.

Let's proceed to step 7:
44 goes into 320 7 times with a remainder of 12.
Use 7 as the next digit of our solution. 
Result so far: 2398.7
If we take 308 away from 320, we end up 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 8:
44 can be fit into 120 2 times, resulting in a remainder of 32.
The number 2 becomes the next digit in our result. 
Result so far: 2398.72
If we take 88 away from 120, we end up 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.

Moving on to step 9:
44 goes into 320 7 times with a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 2398.727
If we take 308 away from 320, we end up 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.

Advancing to step 10:
The number 44 fits into 120 2 times, leaving a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 2398.7272
The remainder is 32 after subtracting 88 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 11:
320 divided by 44 is 7 with a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 2398.72727
If we take 308 away from 320, we end up 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.

Let's proceed to step 12:
If we divide 120 by 44, we get 2 and a remainder of 32.
The next digit of our result is 2. 
Result so far: 2398.727272
Subtracting 88 from 120 leaves us 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.

Step 13:
44 can be fit into 320 7 times, resulting in a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 2398.7272727
If we subtract 308 from 320, 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 14:
The number 44 fits into 120 2 times, leaving a remainder of 32.
The next digit of our result is 2. 
Result so far: 2398.72727272
The remainder is 32 after subtracting 88 from 120.
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 2398.72727272, and the remainder is 3.2e-08.