We're dividing 103217 by 61 
The aim is to understand the frequency of 61 in 103217.

Step 1:
61 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 61

Moving on to step 2:
When dividing 10 by 61, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 61

Advancing to step 3:
When dividing 103 by 61, we get 1 with a remainder of 42.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 42 after subtracting 61 from 103.
Grab the next digit (2) from the dividend, add it to 42, then carry on: 422 / 61

On to step 4:
If we divide 422 by 61, we get 6 and a remainder of 56.
Write down 6 as next digit of the result. 
Result so far: 16.0
If we take 366 away from 422, we end up with 56.
Include the next digit (1) from the dividend after 56, then repeat: 561 / 61

Going ahead to step 5:
If we divide 561 by 61, we get 9 and a remainder of 12.
Write down 9 as next digit of the result. 
Result so far: 169.0
Subtract 549 from 561 to get 12.
Fetch the next digit (7) from the dividend, attach it to 12 and continue: 127 / 61

On to step 6:
61 goes into 127 2 times with a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 1692.0
If we subtract 122 from 127, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 7:
50 divided by 61 is 0 with a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 1692.0
Deduct 0 from 50 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 8:
The number 61 fits into 500 8 times, leaving a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 1692.08
If we subtract 488 from 500, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
If we divide 120 by 61, we get 1 and a remainder of 59.
The next digit of our result is 1. 
Result so far: 1692.081
If we subtract 61 from 120, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 10:
590 divided by 61 is 9 with a remainder of 41.
Record the quotient 9 as the next digit in the result. 
Result so far: 1692.0819
The remainder is 41 after subtracting 549 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 11:
If we divide 410 by 61, we get 6 and a remainder of 44.
The next digit of our result is 6. 
Result so far: 1692.08196
Subtracting 366 from 410 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 12:
440 divided by 61 is 7 with a remainder of 13.
Write down 7 as next digit of the result. 
Result so far: 1692.081967
If we take 427 away from 440, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 13:
When dividing 130 by 61, we get 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 1692.0819672
The remainder is 8 after subtracting 122 from 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
61 goes into 80 1 times with a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 1692.08196721
If we take 61 away from 80, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Our division results in 1692.08196721 with a remaining 1.9e-08.