We're dividing 568642 by 75 
We're looking to find how many times 75 goes into 568642.

Step 1:
When dividing 5 by 75, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 75

Advancing to step 2:
56 divided by 75 is 0 with a remainder of 56.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 56 to get 56.
Take the next digit (8) from the dividend and append it to 56, then repeat: 568 / 75

On to step 3:
If we divide 568 by 75, we get 7 and a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
The remainder is 43 after subtracting 525 from 568.
Bring next digit (6) of the dividend behind the 43 and repeat the process: 436 / 75

Going ahead to step 4:
When dividing 436 by 75, we get 5 with a remainder of 61.
The next digit of our result is 5. 
Result so far: 75.0
Subtract 375 from 436 to get 61.
Bring next digit (4) of the dividend behind the 61 and repeat the process: 614 / 75

Let's proceed to step 5:
614 divided by 75 is 8 with a remainder of 14.
Record the quotient 8 as the next digit in the result. 
Result so far: 758.0
Subtracting 600 from 614 leaves us with 14.
Grab the next digit (2) from the dividend, add it to 14, then carry on: 142 / 75

Going ahead to step 6:
75 can be fit into 142 1 times, resulting in a remainder of 67.
The number 1 becomes the next digit in our result. 
Result so far: 7581.0
Subtracting 75 from 142 leaves us with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Moving on to step 7:
75 goes into 670 8 times with a remainder of 70.
The next digit of our result is 8. 
Result so far: 7581.8
Deduct 600 from 670 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Step 8:
If we divide 700 by 75, we get 9 and a remainder of 25.
The next digit of our result is 9. 
Result so far: 7581.89
Subtract 675 from 700 to 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.

Let's proceed to step 9:
When dividing 250 by 75, we get 3 with a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 7581.893
If we subtract 225 from 250, 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.

Advancing to step 10:
If we divide 250 by 75, we get 3 and a remainder of 25.
The next digit of our result is 3. 
Result so far: 7581.8933
Subtracting 225 from 250 leaves us 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.

In conclusion, the division gives 7581.8933 with a balance of 0.00025.