We're dividing 636569 by 25 
The aim is to understand the frequency of 25 in 636569.

Moving on to step 1:
If we divide 6 by 25, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 25

Advancing to step 2:
The number 25 fits into 63 2 times, leaving a remainder of 13.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
The remainder is 13 after subtracting 50 from 63.
Bring next digit (6) of the dividend behind the 13 and repeat the process: 136 / 25

On to step 3:
When dividing 136 by 25, we get 5 with a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 25.0
If we take 125 away from 136, we end up with 11.
Fetch the next digit (5) from the dividend, attach it to 11 and continue: 115 / 25

On to step 4:
115 divided by 25 is 4 with a remainder of 15.
The number 4 becomes the next digit in our result. 
Result so far: 254.0
Deduct 100 from 115 and we're left with 15.
Take the next digit (6) from the dividend and append it to 15, then repeat: 156 / 25

Let's proceed to step 5:
When dividing 156 by 25, we get 6 with a remainder of 6.
The next digit of our result is 6. 
Result so far: 2546.0
If we take 150 away from 156, we end up with 6.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 25

Going ahead to step 6:
25 goes into 69 2 times with a remainder of 19.
The next digit of our result is 2. 
Result so far: 25462.0
Deduct 50 from 69 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
25 can be fit into 190 7 times, resulting in a remainder of 15.
Write down 7 as next digit of the result. 
Result so far: 25462.7
Subtract 175 from 190 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.

Step 8:
25 goes into 150 6 times with a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 25462.76
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.

On 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: 25462.76
Subtracting 0 from 0 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 10:
0 divided by 25 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 25462.76
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 result is 25462.76 with a remainder of 0.0.