We're dividing 77678 by 41 
The aim is to understand the frequency of 41 in 77678.

Going ahead to step 1:
The number 41 fits into 7 0 times, leaving a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 41

Moving on to step 2:
77 divided by 41 is 1 with a remainder of 36.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 41 from 77, we get 36.
Append the next digit (6) from the dividend to 36 and continue with: 366 / 41

Going ahead to step 3:
41 can be fit into 366 8 times, resulting in a remainder of 38.
Use 8 as the next digit of our solution. 
Result so far: 18.0
If we subtract 328 from 366, we get 38.
Include the next digit (7) from the dividend after 38, then repeat: 387 / 41

Going ahead to step 4:
41 can be fit into 387 9 times, resulting in a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 189.0
If we subtract 369 from 387, we get 18.
Append the next digit (8) from the dividend to 18 and continue with: 188 / 41

Step 5:
41 can be fit into 188 4 times, resulting in a remainder of 24.
The next digit of our result is 4. 
Result so far: 1894.0
If we take 164 away from 188, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 6:
When dividing 240 by 41, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 1894.5
The remainder is 35 after subtracting 205 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 7:
41 can be fit into 350 8 times, resulting in a remainder of 22.
Record the quotient 8 as the next digit in the result. 
Result so far: 1894.58
Subtracting 328 from 350 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.

Going ahead to step 8:
41 can be fit into 220 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 1894.585
If we subtract 205 from 220, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 9:
41 can be fit into 150 3 times, resulting in a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 1894.5853
If we subtract 123 from 150, 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.

Let's proceed to step 10:
If we divide 270 by 41, we get 6 and a remainder of 24.
The next digit of our result is 6. 
Result so far: 1894.58536
Deduct 246 from 270 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 11:
When dividing 240 by 41, we get 5 with a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 1894.585365
Subtract 205 from 240 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 12:
41 goes into 350 8 times with a remainder of 22.
The number 8 becomes the next digit in our result. 
Result so far: 1894.5853658
If we subtract 328 from 350, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 13:
The number 41 fits into 220 5 times, leaving a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 1894.58536585
Subtracting 205 from 220 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The final outcome is 1894.58536585, with a leftover of 1.5e-08.