We look at the division of 397037 by 3 
We want to figure out the number of times 397037 can be divided by 3.

Let's proceed to step 1:
3 divided by 3 is 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 3 from 3 to get 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 3

On to step 2:
When dividing 9 by 3, we get 3 with a remainder of 0.
The next digit of our result is 3. 
Result so far: 13.0
If we take 9 away from 9, we end up with 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 3

Step 3:
When dividing 7 by 3, we get 2 with a remainder of 1.
The next digit of our result is 2. 
Result so far: 132.0
Subtract 6 from 7 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 3

Moving on to step 4:
When dividing 10 by 3, we get 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 1323.0
Subtracting 9 from 10 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 3

On to step 5:
3 goes into 13 4 times with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 13234.0
If we subtract 12 from 13, we get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 3

Let's proceed to step 6:
If we divide 17 by 3, we get 5 and a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 132345.0
Deduct 15 from 17 and we're left 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.

Let's proceed to step 7:
When dividing 20 by 3, we get 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 132345.6
If we take 18 away from 20, 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.

Moving on to step 8:
If we divide 20 by 3, we get 6 and a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 132345.66
If we take 18 away from 20, 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.

In conclusion, the division gives 132345.66 with a balance of 0.002.