We're dividing 779674 by 25 
We're looking to find how many times 25 goes into 779674.

Advancing to step 1:
If we divide 7 by 25, we get 0 and a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 25

Step 2:
25 can be fit into 77 3 times, resulting in a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 3.0
The remainder is 2 after subtracting 75 from 77.
Grab the next digit (9) from the dividend, add it to 2, then carry on: 29 / 25

Moving on to step 3:
When dividing 29 by 25, we get 1 with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 31.0
The remainder is 4 after subtracting 25 from 29.
Include the next digit (6) from the dividend after 4, then repeat: 46 / 25

Let's proceed to step 4:
When dividing 46 by 25, we get 1 with a remainder of 21.
Use 1 as the next digit of our solution. 
Result so far: 311.0
Subtracting 25 from 46 leaves us with 21.
Grab the next digit (7) from the dividend, add it to 21, then carry on: 217 / 25

Step 5:
If we divide 217 by 25, we get 8 and a remainder of 17.
Put 8 as the next digit of the answer. 
Result so far: 3118.0
Subtracting 200 from 217 leaves us with 17.
Append the next digit (4) from the dividend to 17 and continue with: 174 / 25

Step 6:
25 goes into 174 6 times with a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 31186.0
If we take 150 away from 174, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 7:
25 can be fit into 240 9 times, resulting in a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 31186.9
Subtract 225 from 240 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 8:
25 goes into 150 6 times with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 31186.96
Subtracting 150 from 150 leaves us 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.

Let's proceed to step 9:
25 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 31186.96
If we take 0 away from 0, we end up 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.

Step 10:
0 divided by 25 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 31186.96
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.

Our division results in 31186.96 with a remaining 0.0.