145232 ÷ 13 
The aim is to understand the frequency of 13 in 145232.

Advancing to step 1:
1 divided by 13 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 13

On to step 2:
13 goes into 14 1 times with a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 13 from 14 and we're left with 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 13

Step 3:
13 goes into 15 1 times with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we take 13 away from 15, we end up with 2.
Take the next digit (2) from the dividend and append it to 2, then repeat: 22 / 13

Let's proceed to step 4:
22 divided by 13 is 1 with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 111.0
Subtracting 13 from 22 leaves us with 9.
Take the next digit (3) from the dividend and append it to 9, then repeat: 93 / 13

Going ahead to step 5:
If we divide 93 by 13, we get 7 and a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 1117.0
If we take 91 away from 93, we end up with 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 13

Advancing to step 6:
13 goes into 22 1 times with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 11171.0
If we take 13 away from 22, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
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: 11171.6
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 8:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 11171.69
Subtract 117 from 120 to 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.

Going ahead to step 9:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 11171.692
Subtract 26 from 30 to 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 10:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 11171.6923
If we take 39 away from 40, we end up 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.

Moving on to step 11:
When dividing 10 by 13, we get 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 11171.6923
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.

Moving on to step 12:
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: 11171.692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 13:
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: 11171.6923076
If we subtract 78 from 90, we 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 14:
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: 11171.69230769
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.

The quotient of the division is 11171.69230769, and the remainder is 3e-09.