Let's divide 34339 by 3
We're looking to find how many times 3 goes into 34339.

Advancing to step 1:
3 goes into 3 1 times with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 3 away from 3, we end up with 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 3

On to step 2:
When dividing 4 by 3, we get 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 11.0
The remainder is 1 after subtracting 3 from 4.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 3

Going ahead to step 3:
When dividing 13 by 3, we get 4 with a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 114.0
If we subtract 12 from 13, we get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 3

Step 4:
3 goes into 13 4 times with a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 1144.0
Subtract 12 from 13 to get 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 3

Moving on to step 5:
If we divide 19 by 3, we get 6 and a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 11446.0
Subtract 18 from 19 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 6:
If we divide 10 by 3, we get 3 and a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 11446.3
Deduct 9 from 10 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
The number 3 fits into 10 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 11446.33
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 11446.33 and a remainder of 0.001.