349365 ÷ 97 
We're looking to find how many times 97 goes into 349365.

Step 1:
When dividing 3 by 97, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 97

Moving on to step 2:
The number 97 fits into 34 0 times, leaving a remainder of 34.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 34 to get 34.
Append the next digit (9) from the dividend to 34 and continue with: 349 / 97

Let's proceed to step 3:
349 divided by 97 is 3 with a remainder of 58.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtract 291 from 349 to get 58.
Fetch the next digit (3) from the dividend, attach it to 58 and continue: 583 / 97

Let's proceed to step 4:
If we divide 583 by 97, we get 6 and a remainder of 1.
The next digit of our result is 6. 
Result so far: 36.0
Subtract 582 from 583 to get 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 97

Advancing to step 5:
If we divide 16 by 97, we get 0 and a remainder of 16.
Put 0 as the next digit of the answer. 
Result so far: 360.0
Subtract 0 from 16 to get 16.
Include the next digit (5) from the dividend after 16, then repeat: 165 / 97

Moving on to step 6:
97 goes into 165 1 times with a remainder of 68.
Record the quotient 1 as the next digit in the result. 
Result so far: 3601.0
Subtracting 97 from 165 leaves us with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Moving on to step 7:
97 goes into 680 7 times with a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 3601.7
Subtract 679 from 680 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 8:
97 can be fit into 10 0 times, resulting in a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 3601.7
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
97 goes into 100 1 times with a remainder of 3.
The next digit of our result is 1. 
Result so far: 3601.701
If we take 97 away from 100, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 10:
30 divided by 97 is 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 3601.701
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 11:
300 divided by 97 is 3 with a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 3601.70103
Subtracting 291 from 300 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 12:
The number 97 fits into 90 0 times, leaving a remainder of 90.
Put 0 as the next digit of the answer. 
Result so far: 3601.70103
Deduct 0 from 90 and we're left with 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Going ahead to step 13:
The number 97 fits into 900 9 times, leaving a remainder of 27.
The next digit of our result is 9. 
Result so far: 3601.7010309
Subtract 873 from 900 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 14:
270 divided by 97 is 2 with a remainder of 76.
Use 2 as the next digit of our solution. 
Result so far: 3601.70103092
Deduct 194 from 270 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

The final result is 3601.70103092 with a remainder of 7.6e-08.