We look at the division of 77686561 by 503 
The aim is to understand the frequency of 503 in 77686561.

Step 1:
The number 503 fits into 7 0 times, leaving a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 503

Step 2:
When dividing 77 by 503, we get 0 with a remainder of 77.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 77 after subtracting 0 from 77.
Bring next digit (6) of the dividend behind the 77 and repeat the process: 776 / 503

Let's proceed to step 3:
If we divide 776 by 503, we get 1 and a remainder of 273.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 503 from 776 to get 273.
Bring next digit (8) of the dividend behind the 273 and repeat the process: 2738 / 503

On to step 4:
When dividing 2738 by 503, we get 5 with a remainder of 223.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
Deduct 2515 from 2738 and we're left with 223.
Bring next digit (6) of the dividend behind the 223 and repeat the process: 2236 / 503

Going ahead to step 5:
503 goes into 2236 4 times with a remainder of 224.
The number 4 becomes the next digit in our result. 
Result so far: 154.0
The remainder is 224 after subtracting 2012 from 2236.
Fetch the next digit (5) from the dividend, attach it to 224 and continue: 2245 / 503

Let's proceed to step 6:
The number 503 fits into 2245 4 times, leaving a remainder of 233.
Record the quotient 4 as the next digit in the result. 
Result so far: 1544.0
If we subtract 2012 from 2245, we get 233.
Include the next digit (6) from the dividend after 233, then repeat: 2336 / 503

Moving on to step 7:
If we divide 2336 by 503, we get 4 and a remainder of 324.
Put 4 as the next digit of the answer. 
Result so far: 15444.0
If we subtract 2012 from 2336, we get 324.
Take the next digit (1) from the dividend and append it to 324, then repeat: 3241 / 503

Step 8:
503 goes into 3241 6 times with a remainder of 223.
Use 6 as the next digit of our solution. 
Result so far: 154446.0
If we take 3018 away from 3241, we end up with 223.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2230, and continue the process.

Moving on to step 9:
If we divide 2230 by 503, we get 4 and a remainder of 218.
Use 4 as the next digit of our solution. 
Result so far: 154446.4
If we subtract 2012 from 2230, we get 218.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2180, and continue the process.

Step 10:
If we divide 2180 by 503, we get 4 and a remainder of 168.
The number 4 becomes the next digit in our result. 
Result so far: 154446.44
If we subtract 2012 from 2180, we get 168.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1680, and continue the process.

Our division results in 154446.44 with a remaining 0.168.