We're dividing 353597 by 17 
We're looking to find how many times 17 goes into 353597.

Step 1:
17 can be fit into 3 0 times, resulting in 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.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 17

Step 2:
35 divided by 17 is 2 with a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 34 from 35 leaves us with 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 17

Step 3:
The number 17 fits into 13 0 times, leaving a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 20.0
Deduct 0 from 13 and we're left with 13.
Grab the next digit (5) from the dividend, add it to 13, then carry on: 135 / 17

On to step 4:
17 can be fit into 135 7 times, resulting in a remainder of 16.
The number 7 becomes the next digit in our result. 
Result so far: 207.0
If we subtract 119 from 135, we get 16.
Include the next digit (9) from the dividend after 16, then repeat: 169 / 17

Step 5:
17 can be fit into 169 9 times, resulting in a remainder of 16.
Put 9 as the next digit of the answer. 
Result so far: 2079.0
Subtract 153 from 169 to get 16.
Fetch the next digit (7) from the dividend, attach it to 16 and continue: 167 / 17

On to step 6:
The number 17 fits into 167 9 times, leaving a remainder of 14.
Write down 9 as next digit of the result. 
Result so far: 20799.0
Subtracting 153 from 167 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 7:
The number 17 fits into 140 8 times, leaving a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 20799.8
Subtracting 136 from 140 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
40 divided by 17 is 2 with a remainder of 6.
The next digit of our result is 2. 
Result so far: 20799.82
If we take 34 away from 40, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 9:
If we divide 60 by 17, we get 3 and a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 20799.823
Deduct 51 from 60 and we're left 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.

Let's proceed to step 10:
17 goes into 90 5 times with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 20799.8235
If we take 85 away from 90, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
17 goes into 50 2 times with a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 20799.82352
If we take 34 away from 50, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 12:
17 can be fit into 160 9 times, resulting in a remainder of 7.
Use 9 as the next digit of our solution. 
Result so far: 20799.823529
Subtracting 153 from 160 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 13:
When dividing 70 by 17, we get 4 with a remainder of 2.
The next digit of our result is 4. 
Result so far: 20799.8235294
Subtract 68 from 70 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 14:
The number 17 fits into 20 1 times, leaving a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 20799.82352941
The remainder is 3 after subtracting 17 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 20799.82352941 and a remainder of 3e-09.