We're dividing 126879 by 41 
Our goal is to divide 126879 by 41.

Step 1:
When dividing 1 by 41, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 41

On to step 2:
41 can be fit into 12 0 times, resulting in a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 12, we get 12.
Append the next digit (6) from the dividend to 12 and continue with: 126 / 41

Moving on to step 3:
41 goes into 126 3 times with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 3 after subtracting 123 from 126.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 41

Step 4:
When dividing 38 by 41, we get 0 with a remainder of 38.
The next digit of our result is 0. 
Result so far: 30.0
If we take 0 away from 38, we end up with 38.
Bring next digit (7) of the dividend behind the 38 and repeat the process: 387 / 41

Moving on to step 5:
41 goes into 387 9 times with a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 309.0
Subtract 369 from 387 to get 18.
Grab the next digit (9) from the dividend, add it to 18, then carry on: 189 / 41

Going ahead to step 6:
189 divided by 41 is 4 with a remainder of 25.
Record the quotient 4 as the next digit in the result. 
Result so far: 3094.0
Deduct 164 from 189 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 7:
41 can be fit into 250 6 times, resulting in a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 3094.6
Subtract 246 from 250 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 8:
If we divide 40 by 41, we get 0 and a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 3094.6
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 9:
41 can be fit into 400 9 times, resulting in a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 3094.609
Deduct 369 from 400 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 10:
310 divided by 41 is 7 with a remainder of 23.
The next digit of our result is 7. 
Result so far: 3094.6097
Subtract 287 from 310 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 11:
When dividing 230 by 41, we get 5 with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 3094.60975
Subtracting 205 from 230 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 12:
41 can be fit into 250 6 times, resulting in a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 3094.609756
If we take 246 away from 250, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 13:
The number 41 fits into 40 0 times, leaving a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 3094.609756
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 14:
400 divided by 41 is 9 with a remainder of 31.
The next digit of our result is 9. 
Result so far: 3094.60975609
If we subtract 369 from 400, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

The quotient of the division is 3094.60975609, and the remainder is 3.1e-08.