We're dividing 303278 by 35 
We want to figure out the number of times 303278 can be divided by 35.

On to step 1:
35 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
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 / 35

Going ahead to step 2:
When dividing 30 by 35, we get 0 with a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 30, we end up with 30.
Take the next digit (3) from the dividend and append it to 30, then repeat: 303 / 35

On to step 3:
When dividing 303 by 35, we get 8 with a remainder of 23.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtract 280 from 303 to get 23.
Fetch the next digit (2) from the dividend, attach it to 23 and continue: 232 / 35

Going ahead to step 4:
232 divided by 35 is 6 with a remainder of 22.
The next digit of our result is 6. 
Result so far: 86.0
Subtract 210 from 232 to get 22.
Take the next digit (7) from the dividend and append it to 22, then repeat: 227 / 35

Let's proceed to step 5:
227 divided by 35 is 6 with a remainder of 17.
Write down 6 as next digit of the result. 
Result so far: 866.0
The remainder is 17 after subtracting 210 from 227.
Bring next digit (8) of the dividend behind the 17 and repeat the process: 178 / 35

Going ahead to step 6:
When dividing 178 by 35, we get 5 with a remainder of 3.
The next digit of our result is 5. 
Result so far: 8665.0
The remainder is 3 after subtracting 175 from 178.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
35 goes into 30 0 times with a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 8665.0
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 8:
If we divide 300 by 35, we get 8 and a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 8665.08
If we subtract 280 from 300, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
200 divided by 35 is 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 8665.085
Subtracting 175 from 200 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 10:
If we divide 250 by 35, we get 7 and a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 8665.0857
Subtracting 245 from 250 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
The number 35 fits into 50 1 times, leaving a remainder of 15.
Write down 1 as next digit of the result. 
Result so far: 8665.08571
Deduct 35 from 50 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 12:
If we divide 150 by 35, we get 4 and a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 8665.085714
Subtracting 140 from 150 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 13:
If we divide 100 by 35, we get 2 and a remainder of 30.
The next digit of our result is 2. 
Result so far: 8665.0857142
Deduct 70 from 100 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 14:
300 divided by 35 is 8 with a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 8665.08571428
The remainder is 20 after subtracting 280 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Our division results in 8665.08571428 with a remaining 2e-08.