Let's divide 106561 by 45
The aim is to understand the frequency of 45 in 106561.

Step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 45

Moving on to step 2:
45 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 45

Step 3:
45 goes into 106 2 times with a remainder of 16.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtract 90 from 106 to get 16.
Fetch the next digit (5) from the dividend, attach it to 16 and continue: 165 / 45

Advancing to step 4:
45 goes into 165 3 times with a remainder of 30.
The number 3 becomes the next digit in our result. 
Result so far: 23.0
Deduct 135 from 165 and we're left with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 45

Moving on to step 5:
45 goes into 306 6 times with a remainder of 36.
Use 6 as the next digit of our solution. 
Result so far: 236.0
The remainder is 36 after subtracting 270 from 306.
Grab the next digit (1) from the dividend, add it to 36, then carry on: 361 / 45

Advancing to step 6:
361 divided by 45 is 8 with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 2368.0
Deduct 360 from 361 and we're left 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 7:
The number 45 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 2368.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
45 goes into 100 2 times with a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 2368.02
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
45 can be fit into 100 2 times, resulting in a remainder of 10.
The next digit of our result is 2. 
Result so far: 2368.022
Deduct 90 from 100 and we're left 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.

The final result is 2368.022 with a remainder of 0.001.