We're dividing 15759 by 13 
We want to figure out the number of times 15759 can be divided by 13.

Going ahead to step 1:
The number 13 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (5) from the dividend to 1 and continue with: 15 / 13

On to step 2:
13 can be fit into 15 1 times, resulting in a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 13 from 15, we get 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 13

Advancing to step 3:
13 goes into 27 2 times with a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
Subtract 26 from 27 to get 1.
Append the next digit (5) from the dividend to 1 and continue with: 15 / 13

Let's proceed to step 4:
The number 13 fits into 15 1 times, leaving a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 121.0
Subtracting 13 from 15 leaves us with 2.
Include the next digit (9) from the dividend after 2, then repeat: 29 / 13

Step 5:
The number 13 fits into 29 2 times, leaving a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 1212.0
Deduct 26 from 29 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 6:
When dividing 30 by 13, we get 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 1212.2
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.

Let's proceed to step 7:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 1212.23
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.

Advancing to step 8:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 1212.23
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.

Let's proceed to step 9:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The next digit of our result is 7. 
Result so far: 1212.2307
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.

Let's proceed to step 10:
90 divided by 13 is 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 1212.23076
If we take 78 away from 90, we end up 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.

On to step 11:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 1212.230769
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.

Advancing to step 12:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 1212.2307692
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 13:
40 divided by 13 is 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 1212.23076923
Subtract 39 from 40 to 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.

The quotient of the division is 1212.23076923, and the remainder is 1e-09.