829669 ÷ 465 
The aim is to understand the frequency of 465 in 829669.

Moving on to step 1:
The number 465 fits into 8 0 times, leaving a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 465

On to step 2:
When dividing 82 by 465, we get 0 with a remainder of 82.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 82, we end up with 82.
Include the next digit (9) from the dividend after 82, then repeat: 829 / 465

On to step 3:
465 goes into 829 1 times with a remainder of 364.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 465 from 829 and we're left with 364.
Fetch the next digit (6) from the dividend, attach it to 364 and continue: 3646 / 465

Going ahead to step 4:
465 can be fit into 3646 7 times, resulting in a remainder of 391.
Put 7 as the next digit of the answer. 
Result so far: 17.0
The remainder is 391 after subtracting 3255 from 3646.
Append the next digit (6) from the dividend to 391 and continue with: 3916 / 465

Let's proceed to step 5:
If we divide 3916 by 465, we get 8 and a remainder of 196.
The number 8 becomes the next digit in our result. 
Result so far: 178.0
If we subtract 3720 from 3916, we get 196.
Append the next digit (9) from the dividend to 196 and continue with: 1969 / 465

On to step 6:
1969 divided by 465 is 4 with a remainder of 109.
Use 4 as the next digit of our solution. 
Result so far: 1784.0
If we take 1860 away from 1969, we end up with 109.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1090, and continue the process.

Moving on to step 7:
If we divide 1090 by 465, we get 2 and a remainder of 160.
The next digit of our result is 2. 
Result so far: 1784.2
Subtracting 930 from 1090 leaves us with 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1600, and continue the process.

Going ahead to step 8:
465 can be fit into 1600 3 times, resulting in a remainder of 205.
Write down 3 as next digit of the result. 
Result so far: 1784.23
If we subtract 1395 from 1600, we get 205.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2050, and continue the process.

Let's proceed to step 9:
2050 divided by 465 is 4 with a remainder of 190.
Use 4 as the next digit of our solution. 
Result so far: 1784.234
Subtract 1860 from 2050 to get 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1900, and continue the process.

Step 10:
465 can be fit into 1900 4 times, resulting in a remainder of 40.
The next digit of our result is 4. 
Result so far: 1784.2344
Subtract 1860 from 1900 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

In conclusion, the division gives 1784.2344 with a balance of 0.0004.