We're dividing 135877 by 84 
We want to divide 135877 by 84.

Going ahead to step 1:
If we divide 1 by 84, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 84

On to step 2:
The number 84 fits into 13 0 times, leaving a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Grab the next digit (5) from the dividend, add it to 13, then carry on: 135 / 84

Step 3:
84 can be fit into 135 1 times, resulting in a remainder of 51.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 84 from 135 leaves us with 51.
Take the next digit (8) from the dividend and append it to 51, then repeat: 518 / 84

Advancing to step 4:
518 divided by 84 is 6 with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 16.0
If we take 504 away from 518, we end up with 14.
Bring next digit (7) of the dividend behind the 14 and repeat the process: 147 / 84

Moving on to step 5:
The number 84 fits into 147 1 times, leaving a remainder of 63.
The next digit of our result is 1. 
Result so far: 161.0
Deduct 84 from 147 and we're left with 63.
Grab the next digit (7) from the dividend, add it to 63, then carry on: 637 / 84

Going ahead to step 6:
The number 84 fits into 637 7 times, leaving a remainder of 49.
Use 7 as the next digit of our solution. 
Result so far: 1617.0
Subtract 588 from 637 to get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Step 7:
84 can be fit into 490 5 times, resulting in a remainder of 70.
The number 5 becomes the next digit in our result. 
Result so far: 1617.5
Deduct 420 from 490 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 8:
700 divided by 84 is 8 with a remainder of 28.
Record the quotient 8 as the next digit in the result. 
Result so far: 1617.58
The remainder is 28 after subtracting 672 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 9:
280 divided by 84 is 3 with a remainder of 28.
Use 3 as the next digit of our solution. 
Result so far: 1617.583
If we take 252 away from 280, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 10:
84 goes into 280 3 times with a remainder of 28.
Record the quotient 3 as the next digit in the result. 
Result so far: 1617.5833
If we take 252 away from 280, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The final outcome is 1617.5833, with a leftover of 0.00028.