25677 ÷ 17 
Let's see how many times 17 fits into 25677.

On to step 1:
2 divided by 17 is 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 17

Step 2:
When dividing 25 by 17, we get 1 with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 17 from 25 leaves us with 8.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 17

Moving on to step 3:
When dividing 86 by 17, we get 5 with a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 15.0
If we take 85 away from 86, we end up with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 17

On to step 4:
If we divide 17 by 17, we get 1 and a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 151.0
The remainder is 0 after subtracting 17 from 17.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 17

Step 5:
The number 17 fits into 7 0 times, leaving a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 1510.0
If we take 0 away from 7, we end up 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.

Step 6:
When dividing 70 by 17, we get 4 with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 1510.4
Deduct 68 from 70 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
The number 17 fits into 20 1 times, leaving a remainder of 3.
The next digit of our result is 1. 
Result so far: 1510.41
Subtracting 17 from 20 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 8:
The number 17 fits into 30 1 times, leaving a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 1510.411
If we subtract 17 from 30, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final result is 1510.411 with a remainder of 0.0013.