We're dividing 561321 by 34 
We're looking to find how many times 34 goes into 561321.

Let's proceed to 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.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 34

Moving on to step 2:
56 divided by 34 is 1 with a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 34 from 56, we get 22.
Bring next digit (1) of the dividend behind the 22 and repeat the process: 221 / 34

Moving on to step 3:
The number 34 fits into 221 6 times, leaving a remainder of 17.
Put 6 as the next digit of the answer. 
Result so far: 16.0
If we subtract 204 from 221, we get 17.
Append the next digit (3) from the dividend to 17 and continue with: 173 / 34

Moving on to step 4:
The number 34 fits into 173 5 times, leaving a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 165.0
Subtract 170 from 173 to get 3.
Take the next digit (2) from the dividend and append it to 3, then repeat: 32 / 34

Moving on to step 5:
34 goes into 32 0 times with a remainder of 32.
The number 0 becomes the next digit in our result. 
Result so far: 1650.0
Deduct 0 from 32 and we're left with 32.
Append the next digit (1) from the dividend to 32 and continue with: 321 / 34

Step 6:
When dividing 321 by 34, we get 9 with a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 16509.0
Subtract 306 from 321 to 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.

Going ahead to step 7:
150 divided by 34 is 4 with a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 16509.4
Subtracting 136 from 150 leaves us 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.

Moving on to step 8:
34 goes into 140 4 times with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 16509.44
The remainder is 4 after subtracting 136 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 16509.44 and a remainder of 0.004.