We look at the division of 25217 by 83 
We want to figure out the number of times 25217 can be divided by 83.

On to step 1:
When dividing 2 by 83, we get 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 83

Step 2:
83 can be fit into 25 0 times, resulting in a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Include the next digit (2) from the dividend after 25, then repeat: 252 / 83

On to step 3:
252 divided by 83 is 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtract 249 from 252 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 83

On to step 4:
When dividing 31 by 83, we get 0 with a remainder of 31.
Write down 0 as next digit of the result. 
Result so far: 30.0
Subtracting 0 from 31 leaves us with 31.
Grab the next digit (7) from the dividend, add it to 31, then carry on: 317 / 83

Moving on to step 5:
83 can be fit into 317 3 times, resulting in a remainder of 68.
Put 3 as the next digit of the answer. 
Result so far: 303.0
Deduct 249 from 317 and we're left with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Going ahead to step 6:
83 goes into 680 8 times with a remainder of 16.
The next digit of our result is 8. 
Result so far: 303.8
The remainder is 16 after subtracting 664 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 7:
The number 83 fits into 160 1 times, leaving a remainder of 77.
The next digit of our result is 1. 
Result so far: 303.81
The remainder is 77 after subtracting 83 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 770, and continue the process.

Step 8:
When dividing 770 by 83, we get 9 with a remainder of 23.
Put 9 as the next digit of the answer. 
Result so far: 303.819
Deduct 747 from 770 and we're left with 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 9:
When dividing 230 by 83, we get 2 with a remainder of 64.
Use 2 as the next digit of our solution. 
Result so far: 303.8192
The remainder is 64 after subtracting 166 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 10:
640 divided by 83 is 7 with a remainder of 59.
The number 7 becomes the next digit in our result. 
Result so far: 303.81927
If we take 581 away from 640, we end up with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Step 11:
83 goes into 590 7 times with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 303.819277
The remainder is 9 after subtracting 581 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The final result is 303.819277 with a remainder of 9e-07.