507874 ÷ 25 
We're looking to find how many times 25 goes into 507874.

Advancing to step 1:
25 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 25

Step 2:
25 goes into 50 2 times with a remainder of 0.
The next digit of our result is 2. 
Result so far: 2.0
Deduct 50 from 50 and we're left with 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 25

Going ahead to step 3:
25 can be fit into 7 0 times, resulting in a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 20.0
If we take 0 away from 7, we end up with 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 25

Step 4:
The number 25 fits into 78 3 times, leaving a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 203.0
Subtracting 75 from 78 leaves us with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 25

Let's proceed to step 5:
If we divide 37 by 25, we get 1 and a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 2031.0
Subtracting 25 from 37 leaves us with 12.
Take the next digit (4) from the dividend and append it to 12, then repeat: 124 / 25

Step 6:
When dividing 124 by 25, we get 4 with a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 20314.0
Subtracting 100 from 124 leaves us 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.

Advancing to step 7:
When dividing 240 by 25, we get 9 with a remainder of 15.
The next digit of our result is 9. 
Result so far: 20314.9
The remainder is 15 after subtracting 225 from 240.
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:
When dividing 150 by 25, we get 6 with a remainder of 0.
The next digit of our result is 6. 
Result so far: 20314.96
If we take 150 away from 150, 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.

Let's proceed to step 9:
If we divide 0 by 25, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 20314.96
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.

Going ahead to step 10:
If we divide 0 by 25, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 20314.96
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.

In conclusion, the division gives 20314.96 with a balance of 0.0.