We're dividing 77665000 by 409 
The aim is to understand the frequency of 409 in 77665000.

Going ahead to step 1:
When dividing 7 by 409, we get 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 409

Advancing to step 2:
When dividing 77 by 409, we get 0 with a remainder of 77.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 77, we get 77.
Include the next digit (6) from the dividend after 77, then repeat: 776 / 409

Step 3:
776 divided by 409 is 1 with a remainder of 367.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 409 from 776 leaves us with 367.
Bring next digit (6) of the dividend behind the 367 and repeat the process: 3676 / 409

Going ahead to step 4:
409 can be fit into 3676 8 times, resulting in a remainder of 404.
Use 8 as the next digit of our solution. 
Result so far: 18.0
Subtract 3272 from 3676 to get 404.
Grab the next digit (5) from the dividend, add it to 404, then carry on: 4045 / 409

On to step 5:
409 goes into 4045 9 times with a remainder of 364.
Put 9 as the next digit of the answer. 
Result so far: 189.0
Subtracting 3681 from 4045 leaves us with 364.
Fetch the next digit (0) from the dividend, attach it to 364 and continue: 3640 / 409

Moving on to step 6:
If we divide 3640 by 409, we get 8 and a remainder of 368.
Use 8 as the next digit of our solution. 
Result so far: 1898.0
If we take 3272 away from 3640, we end up with 368.
Fetch the next digit (0) from the dividend, attach it to 368 and continue: 3680 / 409

On to step 7:
If we divide 3680 by 409, we get 8 and a remainder of 408.
The number 8 becomes the next digit in our result. 
Result so far: 18988.0
The remainder is 408 after subtracting 3272 from 3680.
Bring next digit (0) of the dividend behind the 408 and repeat the process: 4080 / 409

Advancing to step 8:
409 can be fit into 4080 9 times, resulting in a remainder of 399.
Record the quotient 9 as the next digit in the result. 
Result so far: 189889.0
The remainder is 399 after subtracting 3681 from 4080.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3990, and continue the process.

Advancing to step 9:
When dividing 3990 by 409, we get 9 with a remainder of 309.
The number 9 becomes the next digit in our result. 
Result so far: 189889.9
Subtracting 3681 from 3990 leaves us with 309.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3090, and continue the process.

Advancing to step 10:
The number 409 fits into 3090 7 times, leaving a remainder of 227.
Write down 7 as next digit of the result. 
Result so far: 189889.97
Deduct 2863 from 3090 and we're left with 227.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2270, and continue the process.

Let's proceed to step 11:
409 goes into 2270 5 times with a remainder of 225.
The number 5 becomes the next digit in our result. 
Result so far: 189889.975
Deduct 2045 from 2270 and we're left with 225.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2250, and continue the process.

Advancing to step 12:
2250 divided by 409 is 5 with a remainder of 205.
Record the quotient 5 as the next digit in the result. 
Result so far: 189889.9755
Deduct 2045 from 2250 and we're left with 205.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2050, and continue the process.

The final outcome is 189889.9755, with a leftover of 0.00205.