We look at the division of 353577 by 13 
We want to divide 353577 by 13.

Advancing to step 1:
13 goes into 3 0 times with 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.
Include the next digit (5) from the dividend after 3, then repeat: 35 / 13

Step 2:
35 divided by 13 is 2 with a remainder of 9.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 26 from 35 leaves us with 9.
Fetch the next digit (3) from the dividend, attach it to 9 and continue: 93 / 13

Let's proceed to step 3:
93 divided by 13 is 7 with a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 27.0
If we take 91 away from 93, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 13

Let's proceed to step 4:
If we divide 25 by 13, we get 1 and a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 271.0
Deduct 13 from 25 and we're left with 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 13

On to step 5:
127 divided by 13 is 9 with a remainder of 10.
The number 9 becomes the next digit in our result. 
Result so far: 2719.0
If we take 117 away from 127, we end up with 10.
Bring next digit (7) of the dividend behind the 10 and repeat the process: 107 / 13

Moving on to step 6:
107 divided by 13 is 8 with a remainder of 3.
Put 8 as the next digit of the answer. 
Result so far: 27198.0
Deduct 104 from 107 and we're left 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.

Step 7:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 27198.2
Subtracting 26 from 30 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:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 27198.23
The remainder is 1 after subtracting 39 from 40.
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 9:
If we divide 10 by 13, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 27198.23
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 10:
If we divide 100 by 13, we get 7 and a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 27198.2307
If we take 91 away from 100, we end up 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.

Going ahead to step 11:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 27198.23076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 12:
If we divide 120 by 13, we get 9 and a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 27198.230769
Subtracting 117 from 120 leaves us 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.

Step 13:
When dividing 30 by 13, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 27198.2307692
Deduct 26 from 30 and we're left 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 14:
13 can be fit into 40 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 27198.23076923
If we take 39 away from 40, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Our division results in 27198.23076923 with a remaining 1e-09.