We look at the division of 378032 by 6 
We're looking to find how many times 6 goes into 378032.

Moving on to step 1:
When dividing 3 by 6, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 6

On to step 2:
6 goes into 37 6 times with a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 36 from 37 and we're left with 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 6

Let's proceed to step 3:
6 can be fit into 18 3 times, resulting in a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 63.0
Deduct 18 from 18 and we're left with 0.
Include the next digit (0) from the dividend after 0, then repeat: 0 / 6

On to step 4:
When dividing 0 by 6, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 630.0
If we subtract 0 from 0, we get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 6

On to step 5:
When dividing 3 by 6, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 6300.0
Subtracting 0 from 3 leaves us with 3.
Include the next digit (2) from the dividend after 3, then repeat: 32 / 6

Moving on to step 6:
6 can be fit into 32 5 times, resulting in a remainder of 2.
Put 5 as the next digit of the answer. 
Result so far: 63005.0
If we take 30 away from 32, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
6 goes into 20 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 63005.3
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
When dividing 20 by 6, we get 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 63005.33
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 63005.33 with a balance of 0.002.