Let's divide 100771 by 33
We're looking to find how many times 33 goes into 100771.

Moving on to step 1:
If we divide 1 by 33, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 33

Advancing to step 2:
33 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 33

Step 3:
The number 33 fits into 100 3 times, leaving a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 1 after subtracting 99 from 100.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 33

Advancing to step 4:
33 can be fit into 17 0 times, resulting in a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 30.0
If we subtract 0 from 17, we get 17.
Fetch the next digit (7) from the dividend, attach it to 17 and continue: 177 / 33

Let's proceed to step 5:
If we divide 177 by 33, we get 5 and a remainder of 12.
The number 5 becomes the next digit in our result. 
Result so far: 305.0
Subtracting 165 from 177 leaves us with 12.
Grab the next digit (1) from the dividend, add it to 12, then carry on: 121 / 33

Step 6:
33 can be fit into 121 3 times, resulting in a remainder of 22.
The next digit of our result is 3. 
Result so far: 3053.0
If we take 99 away from 121, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 7:
When dividing 220 by 33, we get 6 with a remainder of 22.
The next digit of our result is 6. 
Result so far: 3053.6
If we take 198 away from 220, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 8:
33 can be fit into 220 6 times, resulting in a remainder of 22.
The next digit of our result is 6. 
Result so far: 3053.66
If we subtract 198 from 220, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

The quotient of the division is 3053.66, and the remainder is 0.022.