Let's divide 34597 by 13
We're looking to find how many times 13 goes into 34597.

Going ahead to step 1:
13 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 subtract 0 from 3, we get 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 13

Let's proceed to step 2:
13 can be fit into 34 2 times, resulting in a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Subtract 26 from 34 to get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 13

Advancing to step 3:
13 can be fit into 85 6 times, resulting in a remainder of 7.
Write down 6 as next digit of the result. 
Result so far: 26.0
Subtract 78 from 85 to get 7.
Include the next digit (9) from the dividend after 7, then repeat: 79 / 13

On to step 4:
13 can be fit into 79 6 times, resulting in a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 266.0
Subtracting 78 from 79 leaves us with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 13

Moving on to step 5:
When dividing 17 by 13, we get 1 with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 2661.0
Subtract 13 from 17 to 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.

Let's proceed to step 6:
13 can be fit into 40 3 times, resulting in a remainder of 1.
The next digit of our result is 3. 
Result so far: 2661.3
If we subtract 39 from 40, we 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.

Step 7:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 2661.3
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 8:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 2661.307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
13 goes into 90 6 times with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 2661.3076
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.

Advancing to step 10:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 2661.30769
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.

Going ahead to step 11:
13 goes into 30 2 times with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 2661.307692
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.

Moving on to step 12:
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: 2661.3076923
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.

Let's proceed to step 13:
When dividing 10 by 13, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 2661.3076923
If we subtract 0 from 10, we 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.

The quotient of the division is 2661.3076923, and the remainder is 1e-08.