15803 ÷ 59 
The aim is to understand the frequency of 59 in 15803.

On to step 1:
59 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
If we subtract 0 from 1, we get 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 59

Step 2:
59 can be fit into 15 0 times, resulting in a remainder of 15.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Bring next digit (8) of the dividend behind the 15 and repeat the process: 158 / 59

Let's proceed to step 3:
When dividing 158 by 59, we get 2 with a remainder of 40.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 118 away from 158, we end up with 40.
Bring next digit (0) of the dividend behind the 40 and repeat the process: 400 / 59

Advancing to step 4:
400 divided by 59 is 6 with a remainder of 46.
Write down 6 as next digit of the result. 
Result so far: 26.0
The remainder is 46 after subtracting 354 from 400.
Include the next digit (3) from the dividend after 46, then repeat: 463 / 59

Step 5:
The number 59 fits into 463 7 times, leaving a remainder of 50.
Use 7 as the next digit of our solution. 
Result so far: 267.0
The remainder is 50 after subtracting 413 from 463.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Let's proceed to step 6:
If we divide 500 by 59, we get 8 and a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 267.8
Deduct 472 from 500 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 7:
The number 59 fits into 280 4 times, leaving a remainder of 44.
Put 4 as the next digit of the answer. 
Result so far: 267.84
If we take 236 away from 280, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 8:
59 goes into 440 7 times with a remainder of 27.
Write down 7 as next digit of the result. 
Result so far: 267.847
If we subtract 413 from 440, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 9:
If we divide 270 by 59, we get 4 and a remainder of 34.
The number 4 becomes the next digit in our result. 
Result so far: 267.8474
If we subtract 236 from 270, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 10:
The number 59 fits into 340 5 times, leaving a remainder of 45.
The number 5 becomes the next digit in our result. 
Result so far: 267.84745
Subtracting 295 from 340 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Step 11:
59 goes into 450 7 times with a remainder of 37.
Use 7 as the next digit of our solution. 
Result so far: 267.847457
Subtracting 413 from 450 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Advancing to step 12:
370 divided by 59 is 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 267.8474576
The remainder is 16 after subtracting 354 from 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 13:
If we divide 160 by 59, we get 2 and a remainder of 42.
Put 2 as the next digit of the answer. 
Result so far: 267.84745762
Subtracting 118 from 160 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final result is 267.84745762 with a remainder of 4.2e-08.