76609587 ÷ 257 
The aim is to understand the frequency of 257 in 76609587.

Advancing to step 1:
If we divide 7 by 257, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 257

Advancing to step 2:
When dividing 76 by 257, we get 0 with a remainder of 76.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 76 to get 76.
Grab the next digit (6) from the dividend, add it to 76, then carry on: 766 / 257

Let's proceed to step 3:
766 divided by 257 is 2 with a remainder of 252.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Deduct 514 from 766 and we're left with 252.
Grab the next digit (0) from the dividend, add it to 252, then carry on: 2520 / 257

Advancing to step 4:
If we divide 2520 by 257, we get 9 and a remainder of 207.
Put 9 as the next digit of the answer. 
Result so far: 29.0
If we subtract 2313 from 2520, we get 207.
Append the next digit (9) from the dividend to 207 and continue with: 2079 / 257

Advancing to step 5:
2079 divided by 257 is 8 with a remainder of 23.
Put 8 as the next digit of the answer. 
Result so far: 298.0
Subtract 2056 from 2079 to get 23.
Grab the next digit (5) from the dividend, add it to 23, then carry on: 235 / 257

Going ahead to step 6:
When dividing 235 by 257, we get 0 with a remainder of 235.
Record the quotient 0 as the next digit in the result. 
Result so far: 2980.0
The remainder is 235 after subtracting 0 from 235.
Take the next digit (8) from the dividend and append it to 235, then repeat: 2358 / 257

Let's proceed to step 7:
The number 257 fits into 2358 9 times, leaving a remainder of 45.
The number 9 becomes the next digit in our result. 
Result so far: 29809.0
Subtract 2313 from 2358 to get 45.
Include the next digit (7) from the dividend after 45, then repeat: 457 / 257

Going ahead to step 8:
457 divided by 257 is 1 with a remainder of 200.
The next digit of our result is 1. 
Result so far: 298091.0
Subtract 257 from 457 to get 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2000, and continue the process.

On to step 9:
257 goes into 2000 7 times with a remainder of 201.
The next digit of our result is 7. 
Result so far: 298091.7
Subtract 1799 from 2000 to get 201.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2010, and continue the process.

Let's proceed to step 10:
257 can be fit into 2010 7 times, resulting in a remainder of 211.
Record the quotient 7 as the next digit in the result. 
Result so far: 298091.77
If we take 1799 away from 2010, we end up with 211.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2110, and continue the process.

The final result is 298091.77 with a remainder of 0.211.