38770416 ÷ 603 
We're looking to find how many times 603 goes into 38770416.

Step 1:
3 divided by 603 is 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (8) from the dividend to 3 and continue with: 38 / 603

On to step 2:
603 goes into 38 0 times with a remainder of 38.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 38 after subtracting 0 from 38.
Bring next digit (7) of the dividend behind the 38 and repeat the process: 387 / 603

On to step 3:
603 can be fit into 387 0 times, resulting in a remainder of 387.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 387 and we're left with 387.
Fetch the next digit (7) from the dividend, attach it to 387 and continue: 3877 / 603

On to step 4:
If we divide 3877 by 603, we get 6 and a remainder of 259.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 3618 away from 3877, we end up with 259.
Append the next digit (0) from the dividend to 259 and continue with: 2590 / 603

On to step 5:
If we divide 2590 by 603, we get 4 and a remainder of 178.
The next digit of our result is 4. 
Result so far: 64.0
If we take 2412 away from 2590, we end up with 178.
Bring next digit (4) of the dividend behind the 178 and repeat the process: 1784 / 603

Advancing to step 6:
The number 603 fits into 1784 2 times, leaving a remainder of 578.
Write down 2 as next digit of the result. 
Result so far: 642.0
Deduct 1206 from 1784 and we're left with 578.
Include the next digit (1) from the dividend after 578, then repeat: 5781 / 603

Advancing to step 7:
The number 603 fits into 5781 9 times, leaving a remainder of 354.
The next digit of our result is 9. 
Result so far: 6429.0
Subtract 5427 from 5781 to get 354.
Take the next digit (6) from the dividend and append it to 354, then repeat: 3546 / 603

Going ahead to step 8:
When dividing 3546 by 603, we get 5 with a remainder of 531.
The number 5 becomes the next digit in our result. 
Result so far: 64295.0
If we subtract 3015 from 3546, we get 531.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5310, and continue the process.

Moving on to step 9:
When dividing 5310 by 603, we get 8 with a remainder of 486.
The number 8 becomes the next digit in our result. 
Result so far: 64295.8
Subtracting 4824 from 5310 leaves us with 486.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4860, and continue the process.

Let's proceed to step 10:
603 goes into 4860 8 times with a remainder of 36.
Put 8 as the next digit of the answer. 
Result so far: 64295.88
Subtracting 4824 from 4860 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

In conclusion, the division gives 64295.88 with a balance of 0.036.