We're dividing 9705634 by 257 
The aim is to understand the frequency of 257 in 9705634.

On to step 1:
The number 257 fits into 9 0 times, leaving a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Grab the next digit (7) from the dividend, add it to 9, then carry on: 97 / 257

Step 2:
When dividing 97 by 257, we get 0 with a remainder of 97.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 97, we end up with 97.
Fetch the next digit (0) from the dividend, attach it to 97 and continue: 970 / 257

Step 3:
The number 257 fits into 970 3 times, leaving a remainder of 199.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 199 after subtracting 771 from 970.
Append the next digit (5) from the dividend to 199 and continue with: 1995 / 257

On to step 4:
If we divide 1995 by 257, we get 7 and a remainder of 196.
Write down 7 as next digit of the result. 
Result so far: 37.0
If we subtract 1799 from 1995, we get 196.
Include the next digit (6) from the dividend after 196, then repeat: 1966 / 257

Step 5:
If we divide 1966 by 257, we get 7 and a remainder of 167.
The number 7 becomes the next digit in our result. 
Result so far: 377.0
If we subtract 1799 from 1966, we get 167.
Append the next digit (3) from the dividend to 167 and continue with: 1673 / 257

Advancing to step 6:
1673 divided by 257 is 6 with a remainder of 131.
The number 6 becomes the next digit in our result. 
Result so far: 3776.0
Deduct 1542 from 1673 and we're left with 131.
Bring next digit (4) of the dividend behind the 131 and repeat the process: 1314 / 257

Going ahead to step 7:
257 goes into 1314 5 times with a remainder of 29.
Write down 5 as next digit of the result. 
Result so far: 37765.0
If we subtract 1285 from 1314, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 8:
If we divide 290 by 257, we get 1 and a remainder of 33.
The number 1 becomes the next digit in our result. 
Result so far: 37765.1
Subtracting 257 from 290 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

On to step 9:
When dividing 330 by 257, we get 1 with a remainder of 73.
Use 1 as the next digit of our solution. 
Result so far: 37765.11
The remainder is 73 after subtracting 257 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

The quotient of the division is 37765.11, and the remainder is 0.073.