15437 ÷ 17 
The aim is to understand the frequency of 17 in 15437.

Step 1:
17 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 17

Going ahead to step 2:
If we divide 15 by 17, we get 0 and a remainder of 15.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Include the next digit (4) from the dividend after 15, then repeat: 154 / 17

Moving on to step 3:
The number 17 fits into 154 9 times, leaving a remainder of 1.
The next digit of our result is 9. 
Result so far: 9.0
Subtracting 153 from 154 leaves us with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 17

On to step 4:
The number 17 fits into 13 0 times, leaving a remainder of 13.
The next digit of our result is 0. 
Result so far: 90.0
Deduct 0 from 13 and we're left with 13.
Bring next digit (7) of the dividend behind the 13 and repeat the process: 137 / 17

Moving on to step 5:
17 goes into 137 8 times with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 908.0
If we take 136 away from 137, 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.

Let's proceed to step 6:
When dividing 10 by 17, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 908.0
Subtracting 0 from 10 leaves us 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.

On to step 7:
The number 17 fits into 100 5 times, leaving a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 908.05
If we take 85 away from 100, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
The number 17 fits into 150 8 times, leaving a remainder of 14.
Record the quotient 8 as the next digit in the result. 
Result so far: 908.058
Subtracting 136 from 150 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 9:
17 can be fit into 140 8 times, resulting in a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 908.0588
Deduct 136 from 140 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 908.0588 and a remainder of 4e-05.