368580 ÷ 34 
We want to figure out the number of times 368580 can be divided by 34.

Moving on to step 1:
3 divided by 34 is 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.
Include the next digit (6) from the dividend after 3, then repeat: 36 / 34

Advancing to step 2:
When dividing 36 by 34, we get 1 with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 34 from 36, we get 2.
Grab the next digit (8) from the dividend, add it to 2, then carry on: 28 / 34

Going ahead to step 3:
The number 34 fits into 28 0 times, leaving a remainder of 28.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 28 and we're left with 28.
Append the next digit (5) from the dividend to 28 and continue with: 285 / 34

Step 4:
The number 34 fits into 285 8 times, leaving a remainder of 13.
Record the quotient 8 as the next digit in the result. 
Result so far: 108.0
Subtract 272 from 285 to get 13.
Grab the next digit (8) from the dividend, add it to 13, then carry on: 138 / 34

Step 5:
34 goes into 138 4 times with a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 1084.0
Subtracting 136 from 138 leaves us with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 34

Moving on to step 6:
34 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 10840.0
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 7:
34 goes into 200 5 times with a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 10840.5
Subtracting 170 from 200 leaves us 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.

Let's proceed to step 8:
The number 34 fits into 300 8 times, leaving a remainder of 28.
The next digit of our result is 8. 
Result so far: 10840.58
Subtract 272 from 300 to 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.

Step 9:
34 can be fit into 280 8 times, resulting in a remainder of 8.
The next digit of our result is 8. 
Result so far: 10840.588
Subtracting 272 from 280 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Our division results in 10840.588 with a remaining 0.0008.