We look at the division of 585745 by 17 
We're looking to find how many times 17 goes into 585745.

Moving on to step 1:
17 goes into 5 0 times with 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 / 17

Advancing to step 2:
The number 17 fits into 58 3 times, leaving a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 51 from 58, we get 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 17

Step 3:
The number 17 fits into 75 4 times, leaving a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 34.0
Subtract 68 from 75 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 17

Advancing to step 4:
When dividing 77 by 17, we get 4 with a remainder of 9.
Write down 4 as next digit of the result. 
Result so far: 344.0
Deduct 68 from 77 and we're left with 9.
Fetch the next digit (4) from the dividend, attach it to 9 and continue: 94 / 17

Step 5:
94 divided by 17 is 5 with a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 3445.0
Deduct 85 from 94 and we're left with 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 17

On to step 6:
The number 17 fits into 95 5 times, leaving a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 34455.0
If we subtract 85 from 95, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
17 can be fit into 100 5 times, resulting in a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 34455.5
If we subtract 85 from 100, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 8:
17 goes into 150 8 times with a remainder of 14.
The next digit of our result is 8. 
Result so far: 34455.58
If we take 136 away from 150, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 9:
The number 17 fits into 140 8 times, leaving a remainder of 4.
The next digit of our result is 8. 
Result so far: 34455.588
Subtract 136 from 140 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 34455.588, and the remainder is 0.0004.