71966 divided by 25 
We're looking to find how many times 25 goes into 71966.

On to step 1:
When dividing 7 by 25, we get 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 25

Moving on to step 2:
25 goes into 71 2 times with a remainder of 21.
The next digit of our result is 2. 
Result so far: 2.0
If we take 50 away from 71, we end up with 21.
Append the next digit (9) from the dividend to 21 and continue with: 219 / 25

Step 3:
If we divide 219 by 25, we get 8 and a remainder of 19.
Write down 8 as next digit of the result. 
Result so far: 28.0
Deduct 200 from 219 and we're left with 19.
Append the next digit (6) from the dividend to 19 and continue with: 196 / 25

Moving on to step 4:
196 divided by 25 is 7 with a remainder of 21.
Write down 7 as next digit of the result. 
Result so far: 287.0
If we subtract 175 from 196, we get 21.
Append the next digit (6) from the dividend to 21 and continue with: 216 / 25

Let's proceed to step 5:
The number 25 fits into 216 8 times, leaving a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 2878.0
Deduct 200 from 216 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 6:
25 can be fit into 160 6 times, resulting in a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 2878.6
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.

On to step 7:
The number 25 fits into 100 4 times, leaving a remainder of 0.
The next digit of our result is 4. 
Result so far: 2878.64
Subtract 100 from 100 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.

Let's proceed to step 8:
0 divided by 25 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 2878.64
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 9:
0 divided by 25 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 2878.64
The remainder is 0 after subtracting 0 from 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 outcome is 2878.64, with a leftover of 0.0.