We're dividing 640564 by 75 
We're looking to find how many times 75 goes into 640564.

Moving on to step 1:
The number 75 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 75

Let's proceed to step 2:
75 goes into 64 0 times with a remainder of 64.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 64, we end up with 64.
Bring next digit (0) of the dividend behind the 64 and repeat the process: 640 / 75

Advancing to step 3:
If we divide 640 by 75, we get 8 and a remainder of 40.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Deduct 600 from 640 and we're left with 40.
Bring next digit (5) of the dividend behind the 40 and repeat the process: 405 / 75

On to step 4:
When dividing 405 by 75, we get 5 with a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 85.0
If we subtract 375 from 405, we get 30.
Take the next digit (6) from the dividend and append it to 30, then repeat: 306 / 75

Let's proceed to step 5:
75 can be fit into 306 4 times, resulting in a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 854.0
If we take 300 away from 306, we end up with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 75

Moving on to step 6:
If we divide 64 by 75, we get 0 and a remainder of 64.
Use 0 as the next digit of our solution. 
Result so far: 8540.0
If we subtract 0 from 64, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 7:
When dividing 640 by 75, we get 8 with a remainder of 40.
Put 8 as the next digit of the answer. 
Result so far: 8540.8
Deduct 600 from 640 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 8:
75 can be fit into 400 5 times, resulting in a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 8540.85
The remainder is 25 after subtracting 375 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 9:
The number 75 fits into 250 3 times, leaving a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 8540.853
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.

Going ahead to step 10:
250 divided by 75 is 3 with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 8540.8533
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.

The final result is 8540.8533 with a remainder of 0.00025.