We're dividing 8121 by 61 
We're looking to find how many times 61 goes into 8121.

Let's proceed to step 1:
8 divided by 61 is 0 with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Include the next digit (1) from the dividend after 8, then repeat: 81 / 61

Moving on to step 2:
If we divide 81 by 61, we get 1 and a remainder of 20.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 61 from 81, we get 20.
Append the next digit (2) from the dividend to 20 and continue with: 202 / 61

Step 3:
The number 61 fits into 202 3 times, leaving a remainder of 19.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 183 from 202, we get 19.
Take the next digit (1) from the dividend and append it to 19, then repeat: 191 / 61

Moving on to step 4:
61 goes into 191 3 times with a remainder of 8.
The next digit of our result is 3. 
Result so far: 133.0
If we take 183 away from 191, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 5:
80 divided by 61 is 1 with a remainder of 19.
Use 1 as the next digit of our solution. 
Result so far: 133.1
Subtract 61 from 80 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 6:
61 goes into 190 3 times with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 133.13
Deduct 183 from 190 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
When dividing 70 by 61, we get 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 133.131
The remainder is 9 after subtracting 61 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
The number 61 fits into 90 1 times, leaving a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 133.1311
The remainder is 29 after subtracting 61 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Our division results in 133.1311 with a remaining 0.00029.