We're dividing 586103 by 44 
We're looking to find how many times 44 goes into 586103.

Let's proceed to step 1:
The number 44 fits into 5 0 times, leaving a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 44

On to step 2:
44 can be fit into 58 1 times, resulting in a remainder of 14.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 44 from 58 leaves us with 14.
Include the next digit (6) from the dividend after 14, then repeat: 146 / 44

On to step 3:
The number 44 fits into 146 3 times, leaving a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtracting 132 from 146 leaves us with 14.
Include the next digit (1) from the dividend after 14, then repeat: 141 / 44

Let's proceed to step 4:
The number 44 fits into 141 3 times, leaving a remainder of 9.
The next digit of our result is 3. 
Result so far: 133.0
Subtract 132 from 141 to get 9.
Bring next digit (0) of the dividend behind the 9 and repeat the process: 90 / 44

Advancing to step 5:
44 can be fit into 90 2 times, resulting in a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 1332.0
Subtracting 88 from 90 leaves us with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 44

Moving on to step 6:
The number 44 fits into 23 0 times, leaving a remainder of 23.
The next digit of our result is 0. 
Result so far: 13320.0
If we take 0 away from 23, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 7:
If we divide 230 by 44, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 13320.5
If we subtract 220 from 230, we 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.

Let's proceed to step 8:
100 divided by 44 is 2 with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 13320.52
The remainder is 12 after subtracting 88 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 9:
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: 13320.522
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.

The final outcome is 13320.522, with a leftover of 0.0032.