377668 ÷ 34 
We want to figure out the number of times 377668 can be divided by 34.

Advancing to step 1:
When dividing 3 by 34, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 34

Step 2:
If we divide 37 by 34, we get 1 and a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 34 from 37, we get 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 34

Step 3:
34 goes into 37 1 times with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 11.0
Subtract 34 from 37 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 34

On to step 4:
When dividing 36 by 34, we get 1 with a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 111.0
Subtract 34 from 36 to get 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 34

On to step 5:
When dividing 26 by 34, we get 0 with a remainder of 26.
Record the quotient 0 as the next digit in the result. 
Result so far: 1110.0
Deduct 0 from 26 and we're left with 26.
Include the next digit (8) from the dividend after 26, then repeat: 268 / 34

Step 6:
268 divided by 34 is 7 with a remainder of 30.
Put 7 as the next digit of the answer. 
Result so far: 11107.0
Subtracting 238 from 268 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.

On to step 7:
If we divide 300 by 34, we get 8 and a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 11107.8
Deduct 272 from 300 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
280 divided by 34 is 8 with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 11107.88
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.

In conclusion, the division gives 11107.88 with a balance of 0.008.