We look at the division of 25177 by 83 
Let's see how many times 83 fits into 25177.

Going ahead to step 1:
When dividing 2 by 83, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 83

Advancing to step 2:
83 goes into 25 0 times with a remainder of 25.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Append the next digit (1) from the dividend to 25 and continue with: 251 / 83

On to step 3:
83 can be fit into 251 3 times, resulting in a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
The remainder is 2 after subtracting 249 from 251.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 83

On to step 4:
27 divided by 83 is 0 with a remainder of 27.
The next digit of our result is 0. 
Result so far: 30.0
Subtract 0 from 27 to get 27.
Grab the next digit (7) from the dividend, add it to 27, then carry on: 277 / 83

Going ahead to step 5:
83 can be fit into 277 3 times, resulting in a remainder of 28.
Put 3 as the next digit of the answer. 
Result so far: 303.0
The remainder is 28 after subtracting 249 from 277.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 6:
If we divide 280 by 83, we get 3 and a remainder of 31.
The number 3 becomes the next digit in our result. 
Result so far: 303.3
The remainder is 31 after subtracting 249 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 7:
83 can be fit into 310 3 times, resulting in a remainder of 61.
Put 3 as the next digit of the answer. 
Result so far: 303.33
Subtract 249 from 310 to get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

The final result is 303.33 with a remainder of 0.061.