We're dividing 565 by 34 
We're looking to find how many times 34 goes into 565.

Step 1:
5 divided by 34 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 34

Let's proceed to step 2:
34 goes into 56 1 times with a remainder of 22.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 34 from 56 to get 22.
Bring next digit (5) of the dividend behind the 22 and repeat the process: 225 / 34

On to step 3:
34 goes into 225 6 times with a remainder of 21.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
Deduct 204 from 225 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 4:
If we divide 210 by 34, we get 6 and a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.6
Deduct 204 from 210 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 5:
The number 34 fits into 60 1 times, leaving a remainder of 26.
Write down 1 as next digit of the result. 
Result so far: 16.61
Deduct 34 from 60 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 6:
If we divide 260 by 34, we get 7 and a remainder of 22.
Put 7 as the next digit of the answer. 
Result so far: 16.617
Subtract 238 from 260 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 7:
220 divided by 34 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 16.6176
If we take 204 away from 220, 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.

Step 8:
34 can be fit into 160 4 times, resulting in a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 16.61764
If we take 136 away from 160, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 9:
240 divided by 34 is 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 16.617647
Subtract 238 from 240 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.

On to step 10:
If we divide 20 by 34, we get 0 and a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 16.617647
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 11:
200 divided by 34 is 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 16.61764705
Subtracting 170 from 200 leaves us 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.

Our division results in 16.61764705 with a remaining 3e-08.