We're dividing 34577 by 13 
Let's see how many times 13 fits into 34577.

Step 1:
13 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 13

Let's proceed to step 2:
The number 13 fits into 34 2 times, leaving a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 2.0
The remainder is 8 after subtracting 26 from 34.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 13

On to step 3:
If we divide 85 by 13, we get 6 and a remainder of 7.
Write down 6 as next digit of the result. 
Result so far: 26.0
Deduct 78 from 85 and we're left with 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 13

Let's proceed to step 4:
13 can be fit into 77 5 times, resulting in a remainder of 12.
Write down 5 as next digit of the result. 
Result so far: 265.0
The remainder is 12 after subtracting 65 from 77.
Bring next digit (7) of the dividend behind the 12 and repeat the process: 127 / 13

Moving on to step 5:
13 can be fit into 127 9 times, resulting in a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 2659.0
The remainder is 10 after subtracting 117 from 127.
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 6:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 2659.7
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
If we divide 90 by 13, we get 6 and a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 2659.76
Deduct 78 from 90 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.

Going ahead to step 8:
When dividing 120 by 13, we get 9 with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 2659.769
Deduct 117 from 120 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.

On to step 9:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 2659.7692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 10:
If we divide 40 by 13, we get 3 and a remainder of 1.
The next digit of our result is 3. 
Result so far: 2659.76923
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 11:
When dividing 10 by 13, we get 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 2659.76923
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.

Advancing to step 12:
13 goes into 100 7 times with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 2659.7692307
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.

Let's proceed to step 13:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 2659.76923076
Deduct 78 from 90 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.

The final outcome is 2659.76923076, with a leftover of 1.2e-08.