We're dividing 340031 by 559 
Let's see how many times 559 fits into 340031.

Let's proceed to step 1:
When dividing 3 by 559, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 559

Moving on to step 2:
559 can be fit into 34 0 times, resulting in a remainder of 34.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 34 and we're left with 34.
Include the next digit (0) from the dividend after 34, then repeat: 340 / 559

Going ahead to step 3:
559 goes into 340 0 times with a remainder of 340.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 340 and we're left with 340.
Bring next digit (0) of the dividend behind the 340 and repeat the process: 3400 / 559

Let's proceed to step 4:
559 goes into 3400 6 times with a remainder of 46.
The next digit of our result is 6. 
Result so far: 6.0
Subtract 3354 from 3400 to get 46.
Bring next digit (3) of the dividend behind the 46 and repeat the process: 463 / 559

Step 5:
If we divide 463 by 559, we get 0 and a remainder of 463.
Put 0 as the next digit of the answer. 
Result so far: 60.0
If we subtract 0 from 463, we get 463.
Take the next digit (1) from the dividend and append it to 463, then repeat: 4631 / 559

On to step 6:
If we divide 4631 by 559, we get 8 and a remainder of 159.
Write down 8 as next digit of the result. 
Result so far: 608.0
If we take 4472 away from 4631, we end up with 159.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1590, and continue the process.

Let's proceed to step 7:
559 can be fit into 1590 2 times, resulting in a remainder of 472.
The next digit of our result is 2. 
Result so far: 608.2
If we subtract 1118 from 1590, we get 472.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4720, and continue the process.

Let's proceed to step 8:
559 can be fit into 4720 8 times, resulting in a remainder of 248.
Write down 8 as next digit of the result. 
Result so far: 608.28
If we subtract 4472 from 4720, we get 248.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2480, and continue the process.

Going ahead to step 9:
2480 divided by 559 is 4 with a remainder of 244.
Use 4 as the next digit of our solution. 
Result so far: 608.284
Subtract 2236 from 2480 to get 244.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2440, and continue the process.

Going ahead to step 10:
559 can be fit into 2440 4 times, resulting in a remainder of 204.
Use 4 as the next digit of our solution. 
Result so far: 608.2844
Deduct 2236 from 2440 and we're left with 204.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2040, and continue the process.

The quotient of the division is 608.2844, and the remainder is 0.00204.