We're dividing 643568 by 75 
We're looking to find how many times 75 goes into 643568.

Let's proceed to step 1:
If we divide 6 by 75, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 75

Going ahead to step 2:
The number 75 fits into 64 0 times, leaving a remainder of 64.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 64 and we're left with 64.
Bring next digit (3) of the dividend behind the 64 and repeat the process: 643 / 75

Moving on to step 3:
643 divided by 75 is 8 with a remainder of 43.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 600 from 643, we get 43.
Grab the next digit (5) from the dividend, add it to 43, then carry on: 435 / 75

Going ahead to step 4:
75 can be fit into 435 5 times, resulting in a remainder of 60.
The number 5 becomes the next digit in our result. 
Result so far: 85.0
Subtracting 375 from 435 leaves us with 60.
Take the next digit (6) from the dividend and append it to 60, then repeat: 606 / 75

Let's proceed to step 5:
75 can be fit into 606 8 times, resulting in a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 858.0
If we take 600 away from 606, we end up with 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 75

Advancing to step 6:
75 can be fit into 68 0 times, resulting in a remainder of 68.
Record the quotient 0 as the next digit in the result. 
Result so far: 8580.0
Subtract 0 from 68 to get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Moving on to step 7:
The number 75 fits into 680 9 times, leaving a remainder of 5.
Use 9 as the next digit of our solution. 
Result so far: 8580.9
Subtracting 675 from 680 leaves us 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.

Moving on to step 8:
If we divide 50 by 75, we get 0 and a remainder of 50.
The next digit of our result is 0. 
Result so far: 8580.9
Deduct 0 from 50 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

On to step 9:
75 goes into 500 6 times with a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 8580.906
Deduct 450 from 500 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 10:
If we divide 500 by 75, we get 6 and a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 8580.9066
The remainder is 50 after subtracting 450 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Our division results in 8580.9066 with a remaining 0.0005.