76569 ÷ 65 
The aim is to understand the frequency of 65 in 76569.

Advancing to step 1:
65 can be fit into 7 0 times, resulting in a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 65

Moving on to step 2:
The number 65 fits into 76 1 times, leaving a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 65 from 76, we get 11.
Bring next digit (5) of the dividend behind the 11 and repeat the process: 115 / 65

Advancing to step 3:
115 divided by 65 is 1 with a remainder of 50.
The next digit of our result is 1. 
Result so far: 11.0
Deduct 65 from 115 and we're left with 50.
Grab the next digit (6) from the dividend, add it to 50, then carry on: 506 / 65

On to step 4:
If we divide 506 by 65, we get 7 and a remainder of 51.
Put 7 as the next digit of the answer. 
Result so far: 117.0
Subtract 455 from 506 to get 51.
Include the next digit (9) from the dividend after 51, then repeat: 519 / 65

Going ahead to step 5:
65 can be fit into 519 7 times, resulting in a remainder of 64.
The number 7 becomes the next digit in our result. 
Result so far: 1177.0
Subtract 455 from 519 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 6:
If we divide 640 by 65, we get 9 and a remainder of 55.
The number 9 becomes the next digit in our result. 
Result so far: 1177.9
If we subtract 585 from 640, 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.

Advancing to step 7:
When dividing 550 by 65, we get 8 with a remainder of 30.
The next digit of our result is 8. 
Result so far: 1177.98
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.

Step 8:
65 can be fit into 300 4 times, resulting in a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 1177.984
The remainder is 40 after subtracting 260 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 9:
The number 65 fits into 400 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 1177.9846
If we take 390 away from 400, we end up with 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 10:
The number 65 fits into 100 1 times, leaving a remainder of 35.
The number 1 becomes the next digit in our result. 
Result so far: 1177.98461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 11:
65 goes into 350 5 times with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 1177.984615
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.

Moving on to step 12:
250 divided by 65 is 3 with a remainder of 55.
The next digit of our result is 3. 
Result so far: 1177.9846153
Subtract 195 from 250 to 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.

Step 13:
65 goes into 550 8 times with a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 1177.98461538
Subtract 520 from 550 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 1177.98461538 with a balance of 3e-08.