We're dividing 17417 by 95 
We want to figure out the number of times 17417 can be divided by 95.

Moving on to step 1:
If we divide 1 by 95, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 95

Step 2:
95 can be fit into 17 0 times, resulting in a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Grab the next digit (4) from the dividend, add it to 17, then carry on: 174 / 95

Going ahead to step 3:
When dividing 174 by 95, we get 1 with a remainder of 79.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 95 away from 174, we end up with 79.
Include the next digit (1) from the dividend after 79, then repeat: 791 / 95

On to step 4:
When dividing 791 by 95, we get 8 with a remainder of 31.
Use 8 as the next digit of our solution. 
Result so far: 18.0
The remainder is 31 after subtracting 760 from 791.
Bring next digit (7) of the dividend behind the 31 and repeat the process: 317 / 95

Step 5:
If we divide 317 by 95, we get 3 and a remainder of 32.
Write down 3 as next digit of the result. 
Result so far: 183.0
If we take 285 away from 317, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 6:
95 goes into 320 3 times with a remainder of 35.
The next digit of our result is 3. 
Result so far: 183.3
Deduct 285 from 320 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 7:
95 goes into 350 3 times with a remainder of 65.
Record the quotient 3 as the next digit in the result. 
Result so far: 183.33
Deduct 285 from 350 and we're left with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The quotient of the division is 183.33, and the remainder is 0.065.