We look at the division of 353217 by 23 
We're looking to find how many times 23 goes into 353217.

Step 1:
23 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 23

On to step 2:
23 can be fit into 35 1 times, resulting in a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 23 from 35 and we're left with 12.
Grab the next digit (3) from the dividend, add it to 12, then carry on: 123 / 23

Let's proceed to step 3:
When dividing 123 by 23, we get 5 with a remainder of 8.
Write down 5 as next digit of the result. 
Result so far: 15.0
Subtract 115 from 123 to get 8.
Append the next digit (2) from the dividend to 8 and continue with: 82 / 23

Moving on to step 4:
If we divide 82 by 23, we get 3 and a remainder of 13.
Use 3 as the next digit of our solution. 
Result so far: 153.0
If we subtract 69 from 82, we get 13.
Append the next digit (1) from the dividend to 13 and continue with: 131 / 23

Moving on to step 5:
23 goes into 131 5 times with a remainder of 16.
The number 5 becomes the next digit in our result. 
Result so far: 1535.0
The remainder is 16 after subtracting 115 from 131.
Bring next digit (7) of the dividend behind the 16 and repeat the process: 167 / 23

Advancing to step 6:
23 goes into 167 7 times with a remainder of 6.
Record the quotient 7 as the next digit in the result. 
Result so far: 15357.0
If we subtract 161 from 167, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
When dividing 60 by 23, we get 2 with a remainder of 14.
Record the quotient 2 as the next digit in the result. 
Result so far: 15357.2
If we subtract 46 from 60, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 8:
If we divide 140 by 23, we get 6 and a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 15357.26
Subtracting 138 from 140 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 9:
23 can be fit into 20 0 times, resulting in a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 15357.26
Subtracting 0 from 20 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 10:
The number 23 fits into 200 8 times, leaving a remainder of 16.
Record the quotient 8 as the next digit in the result. 
Result so far: 15357.2608
Deduct 184 from 200 and we're left 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.

On to step 11:
23 goes into 160 6 times with a remainder of 22.
Record the quotient 6 as the next digit in the result. 
Result so far: 15357.26086
Subtract 138 from 160 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 12:
23 can be fit into 220 9 times, resulting in a remainder of 13.
Put 9 as the next digit of the answer. 
Result so far: 15357.260869
Subtract 207 from 220 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 13:
23 can be fit into 130 5 times, resulting in a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 15357.2608695
If we subtract 115 from 130, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 14:
23 can be fit into 150 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 15357.26086956
Deduct 138 from 150 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Our division results in 15357.26086956 with a remaining 1.2e-08.