We look at the division of 306308 by 16 
We want to figure out the number of times 306308 can be divided by 16.

Step 1:
16 goes into 3 0 times with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Take the next digit (0) from the dividend and append it to 3, then repeat: 30 / 16

Moving on to step 2:
The number 16 fits into 30 1 times, leaving a remainder of 14.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 16 from 30 to get 14.
Append the next digit (6) from the dividend to 14 and continue with: 146 / 16

Advancing to step 3:
When dividing 146 by 16, we get 9 with a remainder of 2.
The next digit of our result is 9. 
Result so far: 19.0
Subtract 144 from 146 to get 2.
Grab the next digit (3) from the dividend, add it to 2, then carry on: 23 / 16

Let's proceed to step 4:
If we divide 23 by 16, we get 1 and a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 191.0
Deduct 16 from 23 and we're left with 7.
Fetch the next digit (0) from the dividend, attach it to 7 and continue: 70 / 16

Step 5:
70 divided by 16 is 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 1914.0
Deduct 64 from 70 and we're left with 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 16

Step 6:
16 goes into 68 4 times with a remainder of 4.
The next digit of our result is 4. 
Result so far: 19144.0
The remainder is 4 after subtracting 64 from 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 7:
16 can be fit into 40 2 times, resulting in a remainder of 8.
The next digit of our result is 2. 
Result so far: 19144.2
The remainder is 8 after subtracting 32 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 8:
The number 16 fits into 80 5 times, leaving a remainder of 0.
The next digit of our result is 5. 
Result so far: 19144.25
The remainder is 0 after subtracting 80 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 9:
0 divided by 16 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 19144.25
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 10:
The number 16 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 19144.25
Subtracting 0 from 0 leaves us with 0.
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 19144.25 with a balance of 0.0.