763637 ÷ 6 
We're looking to find how many times 6 goes into 763637.

Advancing to step 1:
6 goes into 7 1 times with a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 6 from 7, we get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

On to step 2:
6 can be fit into 16 2 times, resulting in a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we subtract 12 from 16, we get 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 6

On to step 3:
The number 6 fits into 43 7 times, leaving a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 127.0
Deduct 42 from 43 and we're left with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 6

Going ahead to step 4:
6 can be fit into 16 2 times, resulting in a remainder of 4.
The next digit of our result is 2. 
Result so far: 1272.0
Subtracting 12 from 16 leaves us with 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 6

Moving on to step 5:
When dividing 43 by 6, we get 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 12727.0
Subtract 42 from 43 to get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 6

Going ahead to step 6:
When dividing 17 by 6, we get 2 with a remainder of 5.
The next digit of our result is 2. 
Result so far: 127272.0
If we take 12 away from 17, 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.

Advancing to step 7:
If we divide 50 by 6, we get 8 and a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 127272.8
Subtract 48 from 50 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.

Let's proceed to step 8:
20 divided by 6 is 3 with a remainder of 2.
The next digit of our result is 3. 
Result so far: 127272.83
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.

Let's proceed to step 9:
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: 127272.833
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.

After the division, we end up with 127272.833 and a remainder of 0.0002.