14114114 divided by 501 
The aim is to understand the frequency of 501 in 14114114.

Let's proceed to step 1:
501 can be fit into 1 0 times, resulting in a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 501

On to step 2:
The number 501 fits into 14 0 times, leaving a remainder of 14.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 14, we get 14.
Take the next digit (1) from the dividend and append it to 14, then repeat: 141 / 501

Step 3:
501 goes into 141 0 times with a remainder of 141.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 141 and we're left with 141.
Take the next digit (1) from the dividend and append it to 141, then repeat: 1411 / 501

On to step 4:
1411 divided by 501 is 2 with a remainder of 409.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 1002 from 1411, we get 409.
Fetch the next digit (4) from the dividend, attach it to 409 and continue: 4094 / 501

Advancing to step 5:
4094 divided by 501 is 8 with a remainder of 86.
The next digit of our result is 8. 
Result so far: 28.0
If we subtract 4008 from 4094, we get 86.
Bring next digit (1) of the dividend behind the 86 and repeat the process: 861 / 501

On to step 6:
501 can be fit into 861 1 times, resulting in a remainder of 360.
The number 1 becomes the next digit in our result. 
Result so far: 281.0
Subtract 501 from 861 to get 360.
Fetch the next digit (1) from the dividend, attach it to 360 and continue: 3601 / 501

On to step 7:
3601 divided by 501 is 7 with a remainder of 94.
The next digit of our result is 7. 
Result so far: 2817.0
Deduct 3507 from 3601 and we're left with 94.
Include the next digit (4) from the dividend after 94, then repeat: 944 / 501

Going ahead to step 8:
944 divided by 501 is 1 with a remainder of 443.
Record the quotient 1 as the next digit in the result. 
Result so far: 28171.0
The remainder is 443 after subtracting 501 from 944.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4430, and continue the process.

Step 9:
The number 501 fits into 4430 8 times, leaving a remainder of 422.
Record the quotient 8 as the next digit in the result. 
Result so far: 28171.8
If we take 4008 away from 4430, we end up with 422.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4220, and continue the process.

Advancing to step 10:
4220 divided by 501 is 8 with a remainder of 212.
Record the quotient 8 as the next digit in the result. 
Result so far: 28171.88
Subtract 4008 from 4220 to get 212.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2120, and continue the process.

In conclusion, the division gives 28171.88 with a balance of 0.212.