We look at the division of 632413 by 6 
We're looking to find how many times 6 goes into 632413.

Let's proceed to step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 6

Step 2:
6 can be fit into 3 0 times, resulting in a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we take 0 away from 3, we end up with 3.
Take the next digit (2) from the dividend and append it to 3, then repeat: 32 / 6

Advancing to step 3:
32 divided by 6 is 5 with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 105.0
If we subtract 30 from 32, we get 2.
Append the next digit (4) from the dividend to 2 and continue with: 24 / 6

On to step 4:
When dividing 24 by 6, we get 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 1054.0
Deduct 24 from 24 and we're left with 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Moving on to step 5:
When dividing 1 by 6, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 10540.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 6

Moving on to step 6:
The number 6 fits into 13 2 times, leaving a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 105402.0
Deduct 12 from 13 and we're left 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.

Going ahead to step 7:
When dividing 10 by 6, we get 1 with a remainder of 4.
The next digit of our result is 1. 
Result so far: 105402.1
Subtracting 6 from 10 leaves us 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 8:
If we divide 40 by 6, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 105402.16
Subtract 36 from 40 to 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.

On to step 9:
40 divided by 6 is 6 with a remainder of 4.
The next digit of our result is 6. 
Result so far: 105402.166
Subtract 36 from 40 to 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.

The final outcome is 105402.166, with a leftover of 0.0004.