We divide 353365 by 34
We want to divide 353365 by 34.

Moving on to step 1:
If we divide 3 by 34, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Include the next digit (5) from the dividend after 3, then repeat: 35 / 34

Step 2:
35 divided by 34 is 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 34 away from 35, we end up with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 34

Step 3:
If we divide 13 by 34, we get 0 and a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 13 after subtracting 0 from 13.
Include the next digit (3) from the dividend after 13, then repeat: 133 / 34

On to step 4:
The number 34 fits into 133 3 times, leaving a remainder of 31.
Put 3 as the next digit of the answer. 
Result so far: 103.0
Subtract 102 from 133 to get 31.
Fetch the next digit (6) from the dividend, attach it to 31 and continue: 316 / 34

On to step 5:
34 goes into 316 9 times with a remainder of 10.
Put 9 as the next digit of the answer. 
Result so far: 1039.0
If we take 306 away from 316, we end up with 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 34

Let's proceed to step 6:
If we divide 105 by 34, we get 3 and a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 10393.0
If we take 102 away from 105, we end up 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 7:
If we divide 30 by 34, we get 0 and a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 10393.0
If we take 0 away from 30, we end up with 30.
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 8:
300 divided by 34 is 8 with a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 10393.08
If we subtract 272 from 300, we 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.

Going ahead to step 9:
The number 34 fits into 280 8 times, leaving a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 10393.088
If we subtract 272 from 280, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 10393.088, and the remainder is 0.0008.