9116603 ÷ 256 
We want to figure out the number of times 9116603 can be divided by 256.

Let's proceed to step 1:
9 divided by 256 is 0 with a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Bring next digit (1) of the dividend behind the 9 and repeat the process: 91 / 256

On to step 2:
If we divide 91 by 256, we get 0 and a remainder of 91.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 91 to get 91.
Fetch the next digit (1) from the dividend, attach it to 91 and continue: 911 / 256

Let's proceed to step 3:
911 divided by 256 is 3 with a remainder of 143.
Use 3 as the next digit of our solution. 
Result so far: 3.0
If we take 768 away from 911, we end up with 143.
Append the next digit (6) from the dividend to 143 and continue with: 1436 / 256

Going ahead to step 4:
If we divide 1436 by 256, we get 5 and a remainder of 156.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
Subtracting 1280 from 1436 leaves us with 156.
Grab the next digit (6) from the dividend, add it to 156, then carry on: 1566 / 256

Moving on to step 5:
1566 divided by 256 is 6 with a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 356.0
If we subtract 1536 from 1566, we get 30.
Grab the next digit (0) from the dividend, add it to 30, then carry on: 300 / 256

Step 6:
The number 256 fits into 300 1 times, leaving a remainder of 44.
Use 1 as the next digit of our solution. 
Result so far: 3561.0
Deduct 256 from 300 and we're left with 44.
Include the next digit (3) from the dividend after 44, then repeat: 443 / 256

On to step 7:
256 goes into 443 1 times with a remainder of 187.
Record the quotient 1 as the next digit in the result. 
Result so far: 35611.0
Deduct 256 from 443 and we're left with 187.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1870, and continue the process.

On to step 8:
The number 256 fits into 1870 7 times, leaving a remainder of 78.
Use 7 as the next digit of our solution. 
Result so far: 35611.7
Subtract 1792 from 1870 to get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Moving on to step 9:
256 can be fit into 780 3 times, resulting in a remainder of 12.
The next digit of our result is 3. 
Result so far: 35611.73
Subtract 768 from 780 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 10:
When dividing 120 by 256, we get 0 with a remainder of 120.
The next digit of our result is 0. 
Result so far: 35611.73
Subtracting 0 from 120 leaves us with 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1200, and continue the process.

Step 11:
256 goes into 1200 4 times with a remainder of 176.
Put 4 as the next digit of the answer. 
Result so far: 35611.7304
Subtract 1024 from 1200 to get 176.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1760, and continue the process.

Step 12:
If we divide 1760 by 256, we get 6 and a remainder of 224.
Use 6 as the next digit of our solution. 
Result so far: 35611.73046
Subtract 1536 from 1760 to get 224.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2240, and continue the process.

Moving on to step 13:
The number 256 fits into 2240 8 times, leaving a remainder of 192.
Record the quotient 8 as the next digit in the result. 
Result so far: 35611.730468
Subtracting 2048 from 2240 leaves us with 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

Advancing to step 14:
256 goes into 1920 7 times with a remainder of 128.
Write down 7 as next digit of the result. 
Result so far: 35611.7304687
Subtracting 1792 from 1920 leaves us with 128.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1280, and continue the process.

Step 15:
256 goes into 1280 5 times with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 35611.73046875
The remainder is 0 after subtracting 1280 from 1280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 35611.73046875 with a balance of 0.0.