We're dividing 679719 by 25 
We're looking to find how many times 25 goes into 679719.

Advancing to step 1:
If we divide 6 by 25, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 25

Step 2:
25 can be fit into 67 2 times, resulting in a remainder of 17.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 50 from 67 leaves us with 17.
Bring next digit (9) of the dividend behind the 17 and repeat the process: 179 / 25

Moving on to step 3:
179 divided by 25 is 7 with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 27.0
Subtract 175 from 179 to get 4.
Take the next digit (7) from the dividend and append it to 4, then repeat: 47 / 25

Moving on to step 4:
47 divided by 25 is 1 with a remainder of 22.
Use 1 as the next digit of our solution. 
Result so far: 271.0
If we subtract 25 from 47, we get 22.
Take the next digit (1) from the dividend and append it to 22, then repeat: 221 / 25

Let's proceed to step 5:
When dividing 221 by 25, we get 8 with a remainder of 21.
The number 8 becomes the next digit in our result. 
Result so far: 2718.0
If we subtract 200 from 221, we get 21.
Append the next digit (9) from the dividend to 21 and continue with: 219 / 25

Going ahead to step 6:
25 can be fit into 219 8 times, resulting in a remainder of 19.
Record the quotient 8 as the next digit in the result. 
Result so far: 27188.0
If we subtract 200 from 219, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
If we divide 190 by 25, we get 7 and a remainder of 15.
The number 7 becomes the next digit in our result. 
Result so far: 27188.7
Deduct 175 from 190 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 8:
If we divide 150 by 25, we get 6 and a remainder of 0.
The next digit of our result is 6. 
Result so far: 27188.76
Deduct 150 from 150 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.

Advancing to step 9:
25 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 27188.76
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.

Going ahead to step 10:
The number 25 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 27188.76
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.

After the division, we end up with 27188.76 and a remainder of 0.0.