We look at the division of 501513 by 61 
The aim is to understand the frequency of 61 in 501513.

Step 1:
When dividing 5 by 61, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 61

Going ahead to step 2:
61 can be fit into 50 0 times, resulting in a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Take the next digit (1) from the dividend and append it to 50, then repeat: 501 / 61

Advancing to step 3:
61 goes into 501 8 times with a remainder of 13.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtracting 488 from 501 leaves us with 13.
Grab the next digit (5) from the dividend, add it to 13, then carry on: 135 / 61

Advancing to step 4:
If we divide 135 by 61, we get 2 and a remainder of 13.
Record the quotient 2 as the next digit in the result. 
Result so far: 82.0
The remainder is 13 after subtracting 122 from 135.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 61

On to step 5:
If we divide 131 by 61, we get 2 and a remainder of 9.
Record the quotient 2 as the next digit in the result. 
Result so far: 822.0
The remainder is 9 after subtracting 122 from 131.
Grab the next digit (3) from the dividend, add it to 9, then carry on: 93 / 61

Step 6:
61 can be fit into 93 1 times, resulting in a remainder of 32.
Record the quotient 1 as the next digit in the result. 
Result so far: 8221.0
Deduct 61 from 93 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
When dividing 320 by 61, we get 5 with a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 8221.5
The remainder is 15 after subtracting 305 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
If we divide 150 by 61, we get 2 and a remainder of 28.
The number 2 becomes the next digit in our result. 
Result so far: 8221.52
Deduct 122 from 150 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 9:
If we divide 280 by 61, we get 4 and a remainder of 36.
The number 4 becomes the next digit in our result. 
Result so far: 8221.524
Subtracting 244 from 280 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 10:
61 goes into 360 5 times with a remainder of 55.
Write down 5 as next digit of the result. 
Result so far: 8221.5245
Deduct 305 from 360 and we're left 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:
61 goes into 550 9 times with a remainder of 1.
The next digit of our result is 9. 
Result so far: 8221.52459
Subtracting 549 from 550 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 12:
The number 61 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 8221.52459
Deduct 0 from 10 and we're left 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.

On to step 13:
When dividing 100 by 61, we get 1 with a remainder of 39.
Record the quotient 1 as the next digit in the result. 
Result so far: 8221.5245901
Deduct 61 from 100 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Let's proceed to step 14:
If we divide 390 by 61, we get 6 and a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 8221.52459016
If we subtract 366 from 390, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Our division results in 8221.52459016 with a remaining 2.4e-08.