111117 ÷ 17 
We want to divide 111117 by 17.

On to step 1:
17 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 17

Advancing to step 2:
17 goes into 11 0 times with a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Append the next digit (1) from the dividend to 11 and continue with: 111 / 17

Advancing to step 3:
17 can be fit into 111 6 times, resulting in a remainder of 9.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 102 from 111 and we're left with 9.
Include the next digit (1) from the dividend after 9, then repeat: 91 / 17

Moving on to step 4:
17 goes into 91 5 times with a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 65.0
The remainder is 6 after subtracting 85 from 91.
Take the next digit (1) from the dividend and append it to 6, then repeat: 61 / 17

On to step 5:
If we divide 61 by 17, we get 3 and a remainder of 10.
Record the quotient 3 as the next digit in the result. 
Result so far: 653.0
If we subtract 51 from 61, we get 10.
Append the next digit (7) from the dividend to 10 and continue with: 107 / 17

Moving on to step 6:
If we divide 107 by 17, we get 6 and a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 6536.0
Subtract 102 from 107 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
When dividing 50 by 17, we get 2 with a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 6536.2
If we take 34 away from 50, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 8:
The number 17 fits into 160 9 times, leaving a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 6536.29
The remainder is 7 after subtracting 153 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
17 can be fit into 70 4 times, resulting in a remainder of 2.
Put 4 as the next digit of the answer. 
Result so far: 6536.294
Subtract 68 from 70 to 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 10:
If we divide 20 by 17, we get 1 and a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 6536.2941
If we subtract 17 from 20, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 11:
17 can be fit into 30 1 times, resulting in a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 6536.29411
If we take 17 away from 30, we end up 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.

The quotient of the division is 6536.29411, and the remainder is 1.3e-05.