We're dividing 109859 by 45 
The aim is to understand the frequency of 45 in 109859.

Step 1:
If we divide 1 by 45, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 45

Moving on to step 2:
45 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (9) from the dividend, attach it to 10 and continue: 109 / 45

Let's proceed to step 3:
45 goes into 109 2 times with a remainder of 19.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we subtract 90 from 109, we get 19.
Append the next digit (8) from the dividend to 19 and continue with: 198 / 45

Advancing to step 4:
45 goes into 198 4 times with a remainder of 18.
The next digit of our result is 4. 
Result so far: 24.0
The remainder is 18 after subtracting 180 from 198.
Fetch the next digit (5) from the dividend, attach it to 18 and continue: 185 / 45

On to step 5:
The number 45 fits into 185 4 times, leaving a remainder of 5.
Use 4 as the next digit of our solution. 
Result so far: 244.0
The remainder is 5 after subtracting 180 from 185.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 45

Moving on to step 6:
The number 45 fits into 59 1 times, leaving a remainder of 14.
The next digit of our result is 1. 
Result so far: 2441.0
If we subtract 45 from 59, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
140 divided by 45 is 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 2441.3
The remainder is 5 after subtracting 135 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
50 divided by 45 is 1 with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 2441.31
If we subtract 45 from 50, we 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.

Let's proceed to step 9:
If we divide 50 by 45, we get 1 and a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 2441.311
If we take 45 away from 50, we end up 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.

The quotient of the division is 2441.311, and the remainder is 0.0005.