We divide 205634 by 75
We want to divide 205634 by 75.

Moving on to step 1:
If we divide 2 by 75, we get 0 and a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Include the next digit (0) from the dividend after 2, then repeat: 20 / 75

Step 2:
When dividing 20 by 75, we get 0 with a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 20, we get 20.
Include the next digit (5) from the dividend after 20, then repeat: 205 / 75

Let's proceed to step 3:
75 can be fit into 205 2 times, resulting in a remainder of 55.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 150 from 205 leaves us with 55.
Include the next digit (6) from the dividend after 55, then repeat: 556 / 75

Going ahead to step 4:
If we divide 556 by 75, we get 7 and a remainder of 31.
Use 7 as the next digit of our solution. 
Result so far: 27.0
If we take 525 away from 556, we end up with 31.
Grab the next digit (3) from the dividend, add it to 31, then carry on: 313 / 75

Going ahead to step 5:
313 divided by 75 is 4 with a remainder of 13.
Use 4 as the next digit of our solution. 
Result so far: 274.0
If we take 300 away from 313, we end up with 13.
Take the next digit (4) from the dividend and append it to 13, then repeat: 134 / 75

Going ahead to step 6:
75 can be fit into 134 1 times, resulting in a remainder of 59.
Record the quotient 1 as the next digit in the result. 
Result so far: 2741.0
Subtract 75 from 134 to get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 7:
75 goes into 590 7 times with a remainder of 65.
Put 7 as the next digit of the answer. 
Result so far: 2741.7
The remainder is 65 after subtracting 525 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Moving on to step 8:
650 divided by 75 is 8 with a remainder of 50.
Use 8 as the next digit of our solution. 
Result so far: 2741.78
The remainder is 50 after subtracting 600 from 650.
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 9:
75 goes into 500 6 times with a remainder of 50.
Put 6 as the next digit of the answer. 
Result so far: 2741.786
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 10:
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: 2741.7866
If we take 450 away from 500, we end up 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.

The quotient of the division is 2741.7866, and the remainder is 0.0005.