We look at the division of 909565 by 87 
The aim is to understand the frequency of 87 in 909565.

Step 1:
If we divide 9 by 87, we get 0 and a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Fetch the next digit (0) from the dividend, attach it to 9 and continue: 90 / 87

Advancing to step 2:
When dividing 90 by 87, we get 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 1.0
If we take 87 away from 90, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 87

Moving on to step 3:
If we divide 39 by 87, we get 0 and a remainder of 39.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we take 0 away from 39, we end up with 39.
Fetch the next digit (5) from the dividend, attach it to 39 and continue: 395 / 87

Moving on to step 4:
395 divided by 87 is 4 with a remainder of 47.
Record the quotient 4 as the next digit in the result. 
Result so far: 104.0
Subtracting 348 from 395 leaves us with 47.
Include the next digit (6) from the dividend after 47, then repeat: 476 / 87

Going ahead to step 5:
The number 87 fits into 476 5 times, leaving a remainder of 41.
Use 5 as the next digit of our solution. 
Result so far: 1045.0
If we subtract 435 from 476, we get 41.
Append the next digit (5) from the dividend to 41 and continue with: 415 / 87

Advancing to step 6:
The number 87 fits into 415 4 times, leaving a remainder of 67.
Use 4 as the next digit of our solution. 
Result so far: 10454.0
If we take 348 away from 415, we end up with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 7:
If we divide 670 by 87, we get 7 and a remainder of 61.
Write down 7 as next digit of the result. 
Result so far: 10454.7
Subtracting 609 from 670 leaves us with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

On to step 8:
87 can be fit into 610 7 times, resulting in a remainder of 1.
The next digit of our result is 7. 
Result so far: 10454.77
Subtract 609 from 610 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final result is 10454.77 with a remainder of 0.001.