We look at the division of 102553 by 65 
The aim is to understand the frequency of 65 in 102553.

On to step 1:
1 divided by 65 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 65

Moving on to step 2:
10 divided by 65 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (2) from the dividend and append it to 10, then repeat: 102 / 65

Step 3:
65 can be fit into 102 1 times, resulting in a remainder of 37.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 65 from 102 to get 37.
Fetch the next digit (5) from the dividend, attach it to 37 and continue: 375 / 65

Moving on to step 4:
65 can be fit into 375 5 times, resulting in a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 15.0
Subtracting 325 from 375 leaves us with 50.
Take the next digit (5) from the dividend and append it to 50, then repeat: 505 / 65

Going ahead to step 5:
65 goes into 505 7 times with a remainder of 50.
Write down 7 as next digit of the result. 
Result so far: 157.0
If we subtract 455 from 505, we get 50.
Append the next digit (3) from the dividend to 50 and continue with: 503 / 65

Advancing to step 6:
The number 65 fits into 503 7 times, leaving a remainder of 48.
Record the quotient 7 as the next digit in the result. 
Result so far: 1577.0
Deduct 455 from 503 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 7:
480 divided by 65 is 7 with a remainder of 25.
Write down 7 as next digit of the result. 
Result so far: 1577.7
Subtracting 455 from 480 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 8:
The number 65 fits into 250 3 times, leaving a remainder of 55.
Write down 3 as next digit of the result. 
Result so far: 1577.73
If we subtract 195 from 250, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

On to step 9:
The number 65 fits into 550 8 times, leaving a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 1577.738
The remainder is 30 after subtracting 520 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 10:
65 can be fit into 300 4 times, resulting in a remainder of 40.
The next digit of our result is 4. 
Result so far: 1577.7384
If we take 260 away from 300, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 11:
65 goes into 400 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 1577.73846
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
When dividing 100 by 65, we get 1 with a remainder of 35.
Write down 1 as next digit of the result. 
Result so far: 1577.738461
Subtracting 65 from 100 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 13:
65 goes into 350 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 1577.7384615
Deduct 325 from 350 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 14:
65 can be fit into 250 3 times, resulting in a remainder of 55.
The next digit of our result is 3. 
Result so far: 1577.73846153
Deduct 195 from 250 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

The final outcome is 1577.73846153, with a leftover of 5.5e-08.