We're dividing 100644 by 75 
We're looking to find how many times 75 goes into 100644.

Advancing to step 1:
When dividing 1 by 75, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 75

Going ahead to step 2:
10 divided by 75 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Include the next digit (0) from the dividend after 10, then repeat: 100 / 75

Let's proceed to step 3:
When dividing 100 by 75, we get 1 with a remainder of 25.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 75 from 100 leaves us with 25.
Append the next digit (6) from the dividend to 25 and continue with: 256 / 75

Advancing to step 4:
When dividing 256 by 75, we get 3 with a remainder of 31.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Subtracting 225 from 256 leaves us with 31.
Bring next digit (4) of the dividend behind the 31 and repeat the process: 314 / 75

Moving on to step 5:
If we divide 314 by 75, we get 4 and a remainder of 14.
Write down 4 as next digit of the result. 
Result so far: 134.0
The remainder is 14 after subtracting 300 from 314.
Take the next digit (4) from the dividend and append it to 14, then repeat: 144 / 75

Going ahead to step 6:
75 goes into 144 1 times with a remainder of 69.
Write down 1 as next digit of the result. 
Result so far: 1341.0
If we take 75 away from 144, we end up with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 7:
75 goes into 690 9 times with a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 1341.9
If we subtract 675 from 690, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 8:
When dividing 150 by 75, we get 2 with a remainder of 0.
The next digit of our result is 2. 
Result so far: 1341.92
If we take 150 away from 150, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 9:
75 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 1341.92
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 10:
75 goes into 0 0 times with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 1341.92
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 1341.92 with a remaining 0.0.