We look at the division of 353424 by 97 
We're looking to find how many times 97 goes into 353424.

Going ahead to step 1:
The number 97 fits into 3 0 times, leaving 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.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 97

Advancing to step 2:
The number 97 fits into 35 0 times, leaving a remainder of 35.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 35 to get 35.
Append the next digit (3) from the dividend to 35 and continue with: 353 / 97

Step 3:
When dividing 353 by 97, we get 3 with a remainder of 62.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 291 from 353 and we're left with 62.
Take the next digit (4) from the dividend and append it to 62, then repeat: 624 / 97

Moving on to step 4:
When dividing 624 by 97, we get 6 with a remainder of 42.
Write down 6 as next digit of the result. 
Result so far: 36.0
If we subtract 582 from 624, we get 42.
Include the next digit (2) from the dividend after 42, then repeat: 422 / 97

Going ahead to step 5:
If we divide 422 by 97, we get 4 and a remainder of 34.
The next digit of our result is 4. 
Result so far: 364.0
If we take 388 away from 422, we end up with 34.
Append the next digit (4) from the dividend to 34 and continue with: 344 / 97

Advancing to step 6:
344 divided by 97 is 3 with a remainder of 53.
Record the quotient 3 as the next digit in the result. 
Result so far: 3643.0
Deduct 291 from 344 and we're left with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

On to step 7:
97 can be fit into 530 5 times, resulting in a remainder of 45.
Record the quotient 5 as the next digit in the result. 
Result so far: 3643.5
Subtracting 485 from 530 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 8:
97 goes into 450 4 times with a remainder of 62.
Write down 4 as next digit of the result. 
Result so far: 3643.54
Subtracting 388 from 450 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Advancing to step 9:
97 can be fit into 620 6 times, resulting in a remainder of 38.
Write down 6 as next digit of the result. 
Result so far: 3643.546
Subtracting 582 from 620 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 10:
380 divided by 97 is 3 with a remainder of 89.
The next digit of our result is 3. 
Result so far: 3643.5463
Deduct 291 from 380 and we're left with 89.
Since there are no more digits in the dividend, we add a zero to the remainder making it 890, and continue the process.

Let's proceed to step 11:
When dividing 890 by 97, we get 9 with a remainder of 17.
Use 9 as the next digit of our solution. 
Result so far: 3643.54639
Subtracting 873 from 890 leaves us with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 12:
97 can be fit into 170 1 times, resulting in a remainder of 73.
Use 1 as the next digit of our solution. 
Result so far: 3643.546391
If we subtract 97 from 170, we get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Let's proceed to step 13:
730 divided by 97 is 7 with a remainder of 51.
Put 7 as the next digit of the answer. 
Result so far: 3643.5463917
Subtracting 679 from 730 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Moving on to step 14:
97 can be fit into 510 5 times, resulting in a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 3643.54639175
Deduct 485 from 510 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

After the division, we end up with 3643.54639175 and a remainder of 2.5e-08.