We're dividing 585578 by 34 
Let's see how many times 34 fits into 585578.

Let's proceed to step 1:
If we divide 5 by 34, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 34

Advancing to step 2:
34 goes into 58 1 times with a remainder of 24.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 34 from 58 and we're left with 24.
Take the next digit (5) from the dividend and append it to 24, then repeat: 245 / 34

Advancing to step 3:
34 goes into 245 7 times with a remainder of 7.
Use 7 as the next digit of our solution. 
Result so far: 17.0
Subtract 238 from 245 to get 7.
Grab the next digit (5) from the dividend, add it to 7, then carry on: 75 / 34

Step 4:
The number 34 fits into 75 2 times, leaving a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 172.0
Subtract 68 from 75 to get 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 34

On to step 5:
34 can be fit into 77 2 times, resulting in a remainder of 9.
Record the quotient 2 as the next digit in the result. 
Result so far: 1722.0
If we subtract 68 from 77, we get 9.
Fetch the next digit (8) from the dividend, attach it to 9 and continue: 98 / 34

Moving on to step 6:
When dividing 98 by 34, we get 2 with a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 17222.0
The remainder is 30 after subtracting 68 from 98.
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 7:
34 can be fit into 300 8 times, resulting in a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 17222.8
Subtract 272 from 300 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
When dividing 280 by 34, we get 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 17222.88
If we take 272 away from 280, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

After the division, we end up with 17222.88 and a remainder of 0.008.