We look at the division of 637111 by 6 
We want to figure out the number of times 637111 can be divided by 6.

Moving on to step 1:
The number 6 fits into 6 1 times, leaving a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 6

Advancing to step 2:
6 can be fit into 3 0 times, resulting in a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we subtract 0 from 3, we get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Going ahead to step 3:
The number 6 fits into 37 6 times, leaving a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 106.0
The remainder is 1 after subtracting 36 from 37.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 6

Moving on to step 4:
6 can be fit into 11 1 times, resulting in a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 1061.0
The remainder is 5 after subtracting 6 from 11.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 6

Step 5:
When dividing 51 by 6, we get 8 with a remainder of 3.
The next digit of our result is 8. 
Result so far: 10618.0
If we subtract 48 from 51, we get 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 6

Let's proceed to step 6:
6 can be fit into 31 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 106185.0
Subtracting 30 from 31 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
The number 6 fits into 10 1 times, leaving a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 106185.1
If we subtract 6 from 10, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 8:
6 can be fit into 40 6 times, resulting in a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 106185.16
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
40 divided by 6 is 6 with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 106185.166
The remainder is 4 after subtracting 36 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 106185.166, with a leftover of 0.0004.