Let's divide 581339 by 17
Our goal is to divide 581339 by 17.

On to step 1:
5 divided by 17 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 17

Advancing to step 2:
The number 17 fits into 58 3 times, leaving a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 7 after subtracting 51 from 58.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 17

Going ahead to step 3:
When dividing 71 by 17, we get 4 with a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 34.0
If we subtract 68 from 71, we get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 17

On to step 4:
33 divided by 17 is 1 with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 341.0
Deduct 17 from 33 and we're left with 16.
Append the next digit (3) from the dividend to 16 and continue with: 163 / 17

On to step 5:
The number 17 fits into 163 9 times, leaving a remainder of 10.
Put 9 as the next digit of the answer. 
Result so far: 3419.0
Subtract 153 from 163 to get 10.
Grab the next digit (9) from the dividend, add it to 10, then carry on: 109 / 17

Going ahead to step 6:
The number 17 fits into 109 6 times, leaving a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 34196.0
If we subtract 102 from 109, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
If we divide 70 by 17, we get 4 and a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 34196.4
If we subtract 68 from 70, we 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.

Advancing to step 8:
20 divided by 17 is 1 with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 34196.41
Deduct 17 from 20 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 9:
If we divide 30 by 17, we get 1 and a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 34196.411
Subtract 17 from 30 to get 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 34196.411, and the remainder is 0.0013.