We're dividing 378674 by 30 
We want to divide 378674 by 30.

Going ahead to step 1:
If we divide 3 by 30, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 30

Moving on to step 2:
When dividing 37 by 30, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 7 after subtracting 30 from 37.
Include the next digit (8) from the dividend after 7, then repeat: 78 / 30

Step 3:
30 can be fit into 78 2 times, resulting in a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
Deduct 60 from 78 and we're left with 18.
Include the next digit (6) from the dividend after 18, then repeat: 186 / 30

Step 4:
186 divided by 30 is 6 with a remainder of 6.
Put 6 as the next digit of the answer. 
Result so far: 126.0
Subtract 180 from 186 to get 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 30

Going ahead to step 5:
When dividing 67 by 30, we get 2 with a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 1262.0
If we subtract 60 from 67, we get 7.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 30

On to step 6:
30 goes into 74 2 times with a remainder of 14.
Put 2 as the next digit of the answer. 
Result so far: 12622.0
The remainder is 14 after subtracting 60 from 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 7:
30 goes into 140 4 times with a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 12622.4
Subtract 120 from 140 to 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.

Step 8:
30 can be fit into 200 6 times, resulting in a remainder of 20.
The next digit of our result is 6. 
Result so far: 12622.46
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
The number 30 fits into 200 6 times, leaving a remainder of 20.
Record the quotient 6 as the next digit in the result. 
Result so far: 12622.466
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 12622.466 with a remainder of 0.002.