We look at the division of 634321 by 75 
We're looking to find how many times 75 goes into 634321.

Going ahead to step 1:
When dividing 6 by 75, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 75

Advancing to step 2:
75 can be fit into 63 0 times, resulting in a remainder of 63.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 63 to get 63.
Fetch the next digit (4) from the dividend, attach it to 63 and continue: 634 / 75

Going ahead to step 3:
If we divide 634 by 75, we get 8 and a remainder of 34.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
The remainder is 34 after subtracting 600 from 634.
Bring next digit (3) of the dividend behind the 34 and repeat the process: 343 / 75

Advancing to step 4:
When dividing 343 by 75, we get 4 with a remainder of 43.
The number 4 becomes the next digit in our result. 
Result so far: 84.0
If we take 300 away from 343, we end up with 43.
Fetch the next digit (2) from the dividend, attach it to 43 and continue: 432 / 75

Going ahead to step 5:
When dividing 432 by 75, we get 5 with a remainder of 57.
The number 5 becomes the next digit in our result. 
Result so far: 845.0
Subtracting 375 from 432 leaves us with 57.
Bring next digit (1) of the dividend behind the 57 and repeat the process: 571 / 75

Moving on to step 6:
75 goes into 571 7 times with a remainder of 46.
Put 7 as the next digit of the answer. 
Result so far: 8457.0
Deduct 525 from 571 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 7:
75 goes into 460 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 8457.6
If we subtract 450 from 460, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
75 can be fit into 100 1 times, resulting in a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 8457.61
If we subtract 75 from 100, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 9:
75 goes into 250 3 times with a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 8457.613
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 10:
When dividing 250 by 75, we get 3 with a remainder of 25.
Use 3 as the next digit of our solution. 
Result so far: 8457.6133
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 8457.6133 with a balance of 0.00025.