Let's divide 127566 by 25
The aim is to understand the frequency of 25 in 127566.

Advancing to step 1:
The number 25 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 25

Step 2:
When dividing 12 by 25, we get 0 with a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 12, we get 12.
Take the next digit (7) from the dividend and append it to 12, then repeat: 127 / 25

On to step 3:
127 divided by 25 is 5 with a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtract 125 from 127 to get 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 25

Going ahead to step 4:
25 divided by 25 is 1 with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 51.0
If we take 25 away from 25, we end up with 0.
Take the next digit (6) from the dividend and append it to 0, then repeat: 6 / 25

Going ahead to step 5:
6 divided by 25 is 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 510.0
If we subtract 0 from 6, we get 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 25

Let's proceed to step 6:
The number 25 fits into 66 2 times, leaving a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 5102.0
If we subtract 50 from 66, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 7:
If we divide 160 by 25, we get 6 and a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 5102.6
Subtract 150 from 160 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
25 can be fit into 100 4 times, resulting in a remainder of 0.
The number 4 becomes the next digit in our result. 
Result so far: 5102.64
Deduct 100 from 100 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.

Let's proceed to step 9:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 5102.64
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.

Moving on to step 10:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 5102.64
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.

Our division results in 5102.64 with a remaining 0.0.