603958 ÷ 97 
We're looking to find how many times 97 goes into 603958.

Going ahead to step 1:
When dividing 6 by 97, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (0) from the dividend after 6, then repeat: 60 / 97

Going ahead to step 2:
97 can be fit into 60 0 times, resulting in a remainder of 60.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 60 leaves us with 60.
Bring next digit (3) of the dividend behind the 60 and repeat the process: 603 / 97

Let's proceed to step 3:
If we divide 603 by 97, we get 6 and a remainder of 21.
The next digit of our result is 6. 
Result so far: 6.0
If we take 582 away from 603, we end up with 21.
Fetch the next digit (9) from the dividend, attach it to 21 and continue: 219 / 97

Moving on to step 4:
97 can be fit into 219 2 times, resulting in a remainder of 25.
Write down 2 as next digit of the result. 
Result so far: 62.0
Deduct 194 from 219 and we're left with 25.
Fetch the next digit (5) from the dividend, attach it to 25 and continue: 255 / 97

Advancing to step 5:
The number 97 fits into 255 2 times, leaving a remainder of 61.
Use 2 as the next digit of our solution. 
Result so far: 622.0
If we take 194 away from 255, we end up with 61.
Include the next digit (8) from the dividend after 61, then repeat: 618 / 97

Going ahead to step 6:
When dividing 618 by 97, we get 6 with a remainder of 36.
Write down 6 as next digit of the result. 
Result so far: 6226.0
Subtracting 582 from 618 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.

Advancing to step 7:
The number 97 fits into 360 3 times, leaving a remainder of 69.
Use 3 as the next digit of our solution. 
Result so far: 6226.3
If we take 291 away from 360, we end up with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Moving on to step 8:
97 can be fit into 690 7 times, resulting in a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 6226.37
Subtract 679 from 690 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 9:
When dividing 110 by 97, we get 1 with a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 6226.371
Deduct 97 from 110 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 10:
When dividing 130 by 97, we get 1 with a remainder of 33.
Write down 1 as next digit of the result. 
Result so far: 6226.3711
If we subtract 97 from 130, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

In conclusion, the division gives 6226.3711 with a balance of 0.00033.