We're dividing 303117 by 17 
Our goal is to divide 303117 by 17.

On to step 1:
When dividing 3 by 17, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 17

Going ahead to step 2:
The number 17 fits into 30 1 times, leaving a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 17 away from 30, we end up with 13.
Fetch the next digit (3) from the dividend, attach it to 13 and continue: 133 / 17

Step 3:
If we divide 133 by 17, we get 7 and a remainder of 14.
The next digit of our result is 7. 
Result so far: 17.0
Deduct 119 from 133 and we're left with 14.
Append the next digit (1) from the dividend to 14 and continue with: 141 / 17

Moving on to step 4:
When dividing 141 by 17, we get 8 with a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 178.0
The remainder is 5 after subtracting 136 from 141.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 17

Moving on to step 5:
When dividing 51 by 17, we get 3 with a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 1783.0
If we take 51 away from 51, we end up with 0.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 17

Step 6:
The number 17 fits into 7 0 times, leaving a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 17830.0
Subtract 0 from 7 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
17 can be fit into 70 4 times, resulting in a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 17830.4
If we subtract 68 from 70, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
20 divided by 17 is 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 17830.41
If we take 17 away from 20, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 9:
17 can be fit into 30 1 times, resulting in a remainder of 13.
The next digit of our result is 1. 
Result so far: 17830.411
Deduct 17 from 30 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Our division results in 17830.411 with a remaining 0.0013.