155642 ÷ 77 
The aim is to understand the frequency of 77 in 155642.

Let's proceed to step 1:
1 divided by 77 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 77

Advancing to step 2:
15 divided by 77 is 0 with a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Bring next digit (5) of the dividend behind the 15 and repeat the process: 155 / 77

Step 3:
If we divide 155 by 77, we get 2 and a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we take 154 away from 155, we end up with 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 77

Advancing to step 4:
If we divide 16 by 77, we get 0 and a remainder of 16.
Put 0 as the next digit of the answer. 
Result so far: 20.0
Subtracting 0 from 16 leaves us with 16.
Grab the next digit (4) from the dividend, add it to 16, then carry on: 164 / 77

Step 5:
164 divided by 77 is 2 with a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 202.0
Subtract 154 from 164 to get 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 77

Let's proceed to step 6:
77 can be fit into 102 1 times, resulting in a remainder of 25.
The next digit of our result is 1. 
Result so far: 2021.0
Deduct 77 from 102 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 7:
When dividing 250 by 77, we get 3 with a remainder of 19.
The next digit of our result is 3. 
Result so far: 2021.3
The remainder is 19 after subtracting 231 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 8:
77 can be fit into 190 2 times, resulting in a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 2021.32
Subtract 154 from 190 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 9:
77 can be fit into 360 4 times, resulting in a remainder of 52.
The number 4 becomes the next digit in our result. 
Result so far: 2021.324
The remainder is 52 after subtracting 308 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 10:
The number 77 fits into 520 6 times, leaving a remainder of 58.
The next digit of our result is 6. 
Result so far: 2021.3246
Deduct 462 from 520 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Going ahead to step 11:
The number 77 fits into 580 7 times, leaving a remainder of 41.
The number 7 becomes the next digit in our result. 
Result so far: 2021.32467
If we subtract 539 from 580, we get 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 12:
77 goes into 410 5 times with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 2021.324675
Subtracting 385 from 410 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 13:
77 goes into 250 3 times with a remainder of 19.
Use 3 as the next digit of our solution. 
Result so far: 2021.3246753
If we take 231 away from 250, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 14:
If we divide 190 by 77, we get 2 and a remainder of 36.
Use 2 as the next digit of our solution. 
Result so far: 2021.32467532
The remainder is 36 after subtracting 154 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

After the division, we end up with 2021.32467532 and a remainder of 3.6e-08.