17789 ÷ 13 
We want to figure out the number of times 17789 can be divided by 13.

Moving on to step 1:
1 divided by 13 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 13

On to step 2:
17 divided by 13 is 1 with a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 13 away from 17, we end up with 4.
Take the next digit (7) from the dividend and append it to 4, then repeat: 47 / 13

Going ahead to step 3:
47 divided by 13 is 3 with a remainder of 8.
Write down 3 as next digit of the result. 
Result so far: 13.0
Deduct 39 from 47 and we're left with 8.
Append the next digit (8) from the dividend to 8 and continue with: 88 / 13

Moving on to step 4:
13 goes into 88 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 136.0
Subtract 78 from 88 to get 10.
Append the next digit (9) from the dividend to 10 and continue with: 109 / 13

Moving on to step 5:
If we divide 109 by 13, we get 8 and a remainder of 5.
Put 8 as the next digit of the answer. 
Result so far: 1368.0
Subtract 104 from 109 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 6:
If we divide 50 by 13, we get 3 and a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 1368.3
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 1368.38
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 1368.384
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
13 goes into 80 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 1368.3846
Subtracting 78 from 80 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 10:
If we divide 20 by 13, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 1368.38461
If we subtract 13 from 20, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 11:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 1368.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 12:
50 divided by 13 is 3 with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 1368.3846153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 13:
If we divide 110 by 13, we get 8 and a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 1368.38461538
Deduct 104 from 110 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The quotient of the division is 1368.38461538, and the remainder is 6e-09.