421721 ÷ 83 
The aim is to understand the frequency of 83 in 421721.

Step 1:
The number 83 fits into 4 0 times, leaving a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 83

Let's proceed to step 2:
The number 83 fits into 42 0 times, leaving a remainder of 42.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Take the next digit (1) from the dividend and append it to 42, then repeat: 421 / 83

Advancing to step 3:
83 goes into 421 5 times with a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 6 after subtracting 415 from 421.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 83

Moving on to step 4:
When dividing 67 by 83, we get 0 with a remainder of 67.
Write down 0 as next digit of the result. 
Result so far: 50.0
Deduct 0 from 67 and we're left with 67.
Grab the next digit (2) from the dividend, add it to 67, then carry on: 672 / 83

On to step 5:
The number 83 fits into 672 8 times, leaving a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 508.0
If we subtract 664 from 672, we get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 83

Advancing to step 6:
When dividing 81 by 83, we get 0 with a remainder of 81.
Write down 0 as next digit of the result. 
Result so far: 5080.0
The remainder is 81 after subtracting 0 from 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Advancing to step 7:
83 goes into 810 9 times with a remainder of 63.
The next digit of our result is 9. 
Result so far: 5080.9
Subtract 747 from 810 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Moving on to step 8:
630 divided by 83 is 7 with a remainder of 49.
The number 7 becomes the next digit in our result. 
Result so far: 5080.97
Subtracting 581 from 630 leaves us with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 9:
If we divide 490 by 83, we get 5 and a remainder of 75.
Record the quotient 5 as the next digit in the result. 
Result so far: 5080.975
Subtracting 415 from 490 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Going ahead to step 10:
83 goes into 750 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 5080.9759
If we subtract 747 from 750, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 11:
The number 83 fits into 30 0 times, leaving a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 5080.9759
Subtracting 0 from 30 leaves us with 30.
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:
83 goes into 300 3 times with a remainder of 51.
The next digit of our result is 3. 
Result so far: 5080.975903
If we take 249 away from 300, we end up with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Advancing to step 13:
If we divide 510 by 83, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 5080.9759036
If we take 498 away from 510, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 14:
83 can be fit into 120 1 times, resulting in a remainder of 37.
Write down 1 as next digit of the result. 
Result so far: 5080.97590361
Subtracting 83 from 120 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

The final result is 5080.97590361 with a remainder of 3.7e-08.