We're dividing 590165 by 13 
Our goal is to divide 590165 by 13.

On to step 1:
The number 13 fits into 5 0 times, leaving 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.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 13

Let's proceed to step 2:
When dividing 59 by 13, we get 4 with a remainder of 7.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 52 from 59 and we're left with 7.
Grab the next digit (0) from the dividend, add it to 7, then carry on: 70 / 13

Advancing to step 3:
13 goes into 70 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 45.0
If we subtract 65 from 70, we get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 13

Moving on to step 4:
The number 13 fits into 51 3 times, leaving a remainder of 12.
Write down 3 as next digit of the result. 
Result so far: 453.0
Subtracting 39 from 51 leaves us with 12.
Fetch the next digit (6) from the dividend, attach it to 12 and continue: 126 / 13

Moving on to step 5:
13 goes into 126 9 times with a remainder of 9.
Write down 9 as next digit of the result. 
Result so far: 4539.0
Deduct 117 from 126 and we're left with 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 13

On to step 6:
13 goes into 95 7 times with a remainder of 4.
Put 7 as the next digit of the answer. 
Result so far: 45397.0
If we subtract 91 from 95, 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 7:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 45397.3
Deduct 39 from 40 and we're left 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.

On to step 8:
10 divided by 13 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 45397.3
Deduct 0 from 10 and we're left 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.

Let's proceed to step 9:
When dividing 100 by 13, we get 7 with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 45397.307
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.

Let's proceed to step 10:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 45397.3076
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.

Let's proceed to step 11:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 45397.30769
If we subtract 117 from 120, we get 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 12:
If we divide 30 by 13, we get 2 and a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 45397.307692
The remainder is 4 after subtracting 26 from 30.
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 13:
When dividing 40 by 13, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 45397.3076923
Subtracting 39 from 40 leaves us 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.

On to step 14:
13 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 45397.3076923
Deduct 0 from 10 and we're left 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.

The final result is 45397.3076923 with a remainder of 1e-08.