Let's divide 25627 by 3
Let's see how many times 3 fits into 25627.

Moving on to step 1:
2 divided by 3 is 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 3

Step 2:
25 divided by 3 is 8 with a remainder of 1.
The next digit of our result is 8. 
Result so far: 8.0
Deduct 24 from 25 and we're left with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 3

Moving on to step 3:
3 goes into 16 5 times with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 85.0
Subtracting 15 from 16 leaves us with 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 3

Let's proceed to step 4:
3 can be fit into 12 4 times, resulting in a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 854.0
If we take 12 away from 12, we end up with 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 3

Moving on to step 5:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 8542.0
Subtracting 6 from 7 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 6:
3 goes into 10 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 8542.3
Subtracting 9 from 10 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
3 goes into 10 3 times with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 8542.33
Deduct 9 from 10 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final outcome is 8542.33, with a leftover of 0.001.