We're dividing 31553 by 6 
Our goal is to divide 31553 by 6.

Going ahead to step 1:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 6

Step 2:
If we divide 31 by 6, we get 5 and a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 30 from 31, we get 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 6

Going ahead to step 3:
When dividing 15 by 6, we get 2 with a remainder of 3.
Record the quotient 2 as the next digit in the result. 
Result so far: 52.0
If we subtract 12 from 15, we get 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 6

Advancing to step 4:
6 can be fit into 35 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 525.0
If we take 30 away from 35, we end up with 5.
Grab the next digit (3) from the dividend, add it to 5, then carry on: 53 / 6

Let's proceed to step 5:
6 goes into 53 8 times with a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 5258.0
Deduct 48 from 53 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 6:
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: 5258.8
Subtracting 48 from 50 leaves us 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.

Moving on to step 7:
6 goes into 20 3 times with a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 5258.83
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.

Advancing to step 8:
6 goes into 20 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 5258.833
Deduct 18 from 20 and we're left 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 5258.833, with a leftover of 0.0002.