157789 ÷ 13 
The aim is to understand the frequency of 13 in 157789.

Moving on to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 13

Let's proceed to step 2:
If we divide 15 by 13, we get 1 and a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 13 from 15 and we're left with 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 13

Let's proceed to step 3:
If we divide 27 by 13, we get 2 and a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 26 from 27 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 13

Going ahead to step 4:
If we divide 17 by 13, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 121.0
If we subtract 13 from 17, we get 4.
Fetch the next digit (8) from the dividend, attach it to 4 and continue: 48 / 13

Advancing to step 5:
13 can be fit into 48 3 times, resulting in a remainder of 9.
Record the quotient 3 as the next digit in the result. 
Result so far: 1213.0
Subtracting 39 from 48 leaves us with 9.
Include the next digit (9) from the dividend after 9, then repeat: 99 / 13

Step 6:
If we divide 99 by 13, we get 7 and a remainder of 8.
Put 7 as the next digit of the answer. 
Result so far: 12137.0
Subtract 91 from 99 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
If we divide 80 by 13, we get 6 and a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 12137.6
If we take 78 away from 80, we end up 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 8:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 12137.61
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 9:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 12137.615
Subtracting 65 from 70 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 10:
If we divide 50 by 13, we get 3 and a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 12137.6153
If we subtract 39 from 50, we get 11.
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 11:
If we divide 110 by 13, we get 8 and a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 12137.61538
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.

Going ahead to step 12:
If we divide 60 by 13, we get 4 and a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 12137.615384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 13:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 12137.6153846
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.

On to step 14:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 12137.61538461
Deduct 13 from 20 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Our division results in 12137.61538461 with a remaining 7e-09.