We're dividing 586103 by 6 
Our goal is to divide 586103 by 6.

Moving on to step 1:
The number 6 fits into 5 0 times, leaving a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 6

Going ahead to step 2:
6 can be fit into 58 9 times, resulting in a remainder of 4.
Put 9 as the next digit of the answer. 
Result so far: 9.0
Deduct 54 from 58 and we're left with 4.
Include the next digit (6) from the dividend after 4, then repeat: 46 / 6

Let's proceed to step 3:
6 goes into 46 7 times with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 97.0
Subtracting 42 from 46 leaves us with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 6

Advancing to step 4:
41 divided by 6 is 6 with a remainder of 5.
The next digit of our result is 6. 
Result so far: 976.0
If we subtract 36 from 41, we get 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 6

On to step 5:
6 can be fit into 50 8 times, resulting in a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 9768.0
Deduct 48 from 50 and we're left with 2.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 6

Let's proceed to step 6:
6 can be fit into 23 3 times, resulting in a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 97683.0
If we subtract 18 from 23, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
The number 6 fits into 50 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 97683.8
If we take 48 away from 50, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
6 goes into 20 3 times with a remainder of 2.
The next digit of our result is 3. 
Result so far: 97683.83
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 9:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 97683.833
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final outcome is 97683.833, with a leftover of 0.0002.