590123 ÷ 65 
The aim is to understand the frequency of 65 in 590123.

Going ahead to step 1:
65 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 65

Advancing to step 2:
If we divide 59 by 65, we get 0 and a remainder of 59.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 59 to get 59.
Include the next digit (0) from the dividend after 59, then repeat: 590 / 65

Moving on to step 3:
When dividing 590 by 65, we get 9 with a remainder of 5.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
If we take 585 away from 590, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 65

Moving on to step 4:
When dividing 51 by 65, we get 0 with a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 90.0
If we take 0 away from 51, we end up with 51.
Fetch the next digit (2) from the dividend, attach it to 51 and continue: 512 / 65

Let's proceed to step 5:
The number 65 fits into 512 7 times, leaving a remainder of 57.
Put 7 as the next digit of the answer. 
Result so far: 907.0
Subtract 455 from 512 to get 57.
Include the next digit (3) from the dividend after 57, then repeat: 573 / 65

Going ahead to step 6:
65 goes into 573 8 times with a remainder of 53.
The next digit of our result is 8. 
Result so far: 9078.0
The remainder is 53 after subtracting 520 from 573.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Step 7:
The number 65 fits into 530 8 times, leaving a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 9078.8
Subtracting 520 from 530 leaves us 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.

Let's proceed to step 8:
100 divided by 65 is 1 with a remainder of 35.
Record the quotient 1 as the next digit in the result. 
Result so far: 9078.81
If we take 65 away from 100, we end up 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 9:
When dividing 350 by 65, we get 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 9078.815
The remainder is 25 after subtracting 325 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 10:
If we divide 250 by 65, we get 3 and a remainder of 55.
Write down 3 as next digit of the result. 
Result so far: 9078.8153
If we take 195 away from 250, we end up 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.

Let's proceed to step 11:
65 goes into 550 8 times with a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 9078.81538
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.

Let's proceed to step 12:
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: 9078.815384
Subtracting 260 from 300 leaves us 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.

Step 13:
65 goes into 400 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 9078.8153846
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.

Moving on to step 14:
65 goes into 100 1 times with a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 9078.81538461
Deduct 65 from 100 and we're left 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.

In conclusion, the division gives 9078.81538461 with a balance of 3.5e-08.