We look at the division of 597661 by 13 
We're looking to find how many times 13 goes into 597661.

Going ahead to step 1:
13 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (9) from the dividend after 5, then repeat: 59 / 13

Let's proceed to step 2:
59 divided by 13 is 4 with a remainder of 7.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 7 after subtracting 52 from 59.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 13

Let's proceed to step 3:
When dividing 77 by 13, we get 5 with a remainder of 12.
Put 5 as the next digit of the answer. 
Result so far: 45.0
Deduct 65 from 77 and we're left with 12.
Grab the next digit (6) from the dividend, add it to 12, then carry on: 126 / 13

Step 4:
When dividing 126 by 13, we get 9 with a remainder of 9.
The next digit of our result is 9. 
Result so far: 459.0
If we subtract 117 from 126, we get 9.
Append the next digit (6) from the dividend to 9 and continue with: 96 / 13

Let's proceed to step 5:
The number 13 fits into 96 7 times, leaving a remainder of 5.
The next digit of our result is 7. 
Result so far: 4597.0
Deduct 91 from 96 and we're left with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 13

Let's proceed to step 6:
If we divide 51 by 13, we get 3 and a remainder of 12.
The next digit of our result is 3. 
Result so far: 45973.0
Subtract 39 from 51 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.

Advancing to step 7:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 45973.9
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.

Advancing to step 8:
13 goes into 30 2 times with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 45973.92
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.

Going ahead to step 9:
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: 45973.923
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.

Going ahead to step 10:
10 divided by 13 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 45973.923
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 11:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 45973.92307
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.

On to step 12:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 45973.923076
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 13:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 45973.9230769
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.

Advancing to step 14:
30 divided by 13 is 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 45973.92307692
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.

Our division results in 45973.92307692 with a remaining 4e-09.