137471 ÷ 6 
We're looking to find how many times 6 goes into 137471.

Going ahead to step 1:
1 divided by 6 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 6

Step 2:
If we divide 13 by 6, we get 2 and a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 12 from 13, we get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 6

Moving on to step 3:
If we divide 17 by 6, we get 2 and a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 22.0
Deduct 12 from 17 and we're left with 5.
Take the next digit (4) from the dividend and append it to 5, then repeat: 54 / 6

Let's proceed to step 4:
When dividing 54 by 6, we get 9 with a remainder of 0.
Record the quotient 9 as the next digit in the result. 
Result so far: 229.0
Subtracting 54 from 54 leaves us with 0.
Append the next digit (7) from the dividend to 0 and continue with: 7 / 6

Advancing to step 5:
6 can be fit into 7 1 times, resulting in a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 2291.0
If we subtract 6 from 7, we get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 6

Moving on to step 6:
The number 6 fits into 11 1 times, leaving a remainder of 5.
The next digit of our result is 1. 
Result so far: 22911.0
If we take 6 away from 11, we end up 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.

Moving on to step 7:
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: 22911.8
Deduct 48 from 50 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.

Going ahead to step 8:
When dividing 20 by 6, we get 3 with a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 22911.83
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.

On to step 9:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 22911.833
Subtracting 18 from 20 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.

In conclusion, the division gives 22911.833 with a balance of 0.0002.