We're dividing 186577 by 42 
The aim is to understand the frequency of 42 in 186577.

Let's proceed to step 1:
When dividing 1 by 42, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 42

Going ahead to step 2:
When dividing 18 by 42, we get 0 with a remainder of 18.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 18 after subtracting 0 from 18.
Grab the next digit (6) from the dividend, add it to 18, then carry on: 186 / 42

Moving on to step 3:
The number 42 fits into 186 4 times, leaving a remainder of 18.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 168 from 186 and we're left with 18.
Bring next digit (5) of the dividend behind the 18 and repeat the process: 185 / 42

On to step 4:
42 goes into 185 4 times with a remainder of 17.
The next digit of our result is 4. 
Result so far: 44.0
Subtracting 168 from 185 leaves us with 17.
Bring next digit (7) of the dividend behind the 17 and repeat the process: 177 / 42

Advancing to step 5:
When dividing 177 by 42, we get 4 with a remainder of 9.
The number 4 becomes the next digit in our result. 
Result so far: 444.0
The remainder is 9 after subtracting 168 from 177.
Bring next digit (7) of the dividend behind the 9 and repeat the process: 97 / 42

Step 6:
When dividing 97 by 42, we get 2 with a remainder of 13.
The number 2 becomes the next digit in our result. 
Result so far: 4442.0
Subtracting 84 from 97 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 7:
42 goes into 130 3 times with a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 4442.3
If we take 126 away from 130, we end up 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.

Advancing to step 8:
The number 42 fits into 40 0 times, leaving a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 4442.3
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 9:
If we divide 400 by 42, we get 9 and a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 4442.309
Subtracting 378 from 400 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 10:
If we divide 220 by 42, we get 5 and a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 4442.3095
Deduct 210 from 220 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.

Step 11:
The number 42 fits into 100 2 times, leaving a remainder of 16.
The next digit of our result is 2. 
Result so far: 4442.30952
Subtract 84 from 100 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 12:
42 can be fit into 160 3 times, resulting in a remainder of 34.
The number 3 becomes the next digit in our result. 
Result so far: 4442.309523
Deduct 126 from 160 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
340 divided by 42 is 8 with a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 4442.3095238
The remainder is 4 after subtracting 336 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 14:
The number 42 fits into 40 0 times, leaving a remainder of 40.
The next digit of our result is 0. 
Result so far: 4442.3095238
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 4442.3095238, and the remainder is 4e-08.