Let's divide 177666 by 25
We want to divide 177666 by 25.

Going ahead to step 1:
25 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 25

Advancing to step 2:
25 can be fit into 17 0 times, resulting in a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Include the next digit (7) from the dividend after 17, then repeat: 177 / 25

Going ahead to step 3:
177 divided by 25 is 7 with a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 175 from 177 leaves us with 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 25

On to step 4:
25 goes into 26 1 times with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 71.0
Subtracting 25 from 26 leaves us with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 25

Step 5:
25 goes into 16 0 times with a remainder of 16.
Write down 0 as next digit of the result. 
Result so far: 710.0
Subtracting 0 from 16 leaves us with 16.
Fetch the next digit (6) from the dividend, attach it to 16 and continue: 166 / 25

Step 6:
25 goes into 166 6 times with a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 7106.0
The remainder is 16 after subtracting 150 from 166.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 7:
The number 25 fits into 160 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 7106.6
The remainder is 10 after subtracting 150 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
When dividing 100 by 25, we get 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 7106.64
The remainder is 0 after subtracting 100 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 9:
25 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 7106.64
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 10:
0 divided by 25 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 7106.64
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 7106.64 with a remainder of 0.0.