We look at the division of 16821377 by 565 
The aim is to understand the frequency of 565 in 16821377.

Step 1:
When dividing 1 by 565, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 565

Advancing to step 2:
16 divided by 565 is 0 with a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 16 and we're left with 16.
Take the next digit (8) from the dividend and append it to 16, then repeat: 168 / 565

Advancing to step 3:
565 goes into 168 0 times with a remainder of 168.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 168, we get 168.
Grab the next digit (2) from the dividend, add it to 168, then carry on: 1682 / 565

Going ahead to step 4:
When dividing 1682 by 565, we get 2 with a remainder of 552.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 1130 away from 1682, we end up with 552.
Grab the next digit (1) from the dividend, add it to 552, then carry on: 5521 / 565

Moving on to step 5:
The number 565 fits into 5521 9 times, leaving a remainder of 436.
The number 9 becomes the next digit in our result. 
Result so far: 29.0
Deduct 5085 from 5521 and we're left with 436.
Grab the next digit (3) from the dividend, add it to 436, then carry on: 4363 / 565

Moving on to step 6:
565 can be fit into 4363 7 times, resulting in a remainder of 408.
Put 7 as the next digit of the answer. 
Result so far: 297.0
The remainder is 408 after subtracting 3955 from 4363.
Fetch the next digit (7) from the dividend, attach it to 408 and continue: 4087 / 565

Advancing to step 7:
The number 565 fits into 4087 7 times, leaving a remainder of 132.
Put 7 as the next digit of the answer. 
Result so far: 2977.0
If we subtract 3955 from 4087, we get 132.
Take the next digit (7) from the dividend and append it to 132, then repeat: 1327 / 565

Advancing to step 8:
When dividing 1327 by 565, we get 2 with a remainder of 197.
Use 2 as the next digit of our solution. 
Result so far: 29772.0
Subtract 1130 from 1327 to get 197.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1970, and continue the process.

Moving on to step 9:
565 goes into 1970 3 times with a remainder of 275.
The next digit of our result is 3. 
Result so far: 29772.3
Subtract 1695 from 1970 to get 275.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2750, and continue the process.

Going ahead to step 10:
The number 565 fits into 2750 4 times, leaving a remainder of 490.
Record the quotient 4 as the next digit in the result. 
Result so far: 29772.34
If we subtract 2260 from 2750, we get 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4900, and continue the process.

Going ahead to step 11:
The number 565 fits into 4900 8 times, leaving a remainder of 380.
Put 8 as the next digit of the answer. 
Result so far: 29772.348
The remainder is 380 after subtracting 4520 from 4900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3800, and continue the process.

Let's proceed to step 12:
565 goes into 3800 6 times with a remainder of 410.
Use 6 as the next digit of our solution. 
Result so far: 29772.3486
If we take 3390 away from 3800, we end up with 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4100, and continue the process.

Going ahead to step 13:
The number 565 fits into 4100 7 times, leaving a remainder of 145.
Write down 7 as next digit of the result. 
Result so far: 29772.34867
The remainder is 145 after subtracting 3955 from 4100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1450, and continue the process.

Going ahead to step 14:
565 can be fit into 1450 2 times, resulting in a remainder of 320.
Record the quotient 2 as the next digit in the result. 
Result so far: 29772.348672
If we subtract 1130 from 1450, we get 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3200, and continue the process.

Advancing to step 15:
When dividing 3200 by 565, we get 5 with a remainder of 375.
Use 5 as the next digit of our solution. 
Result so far: 29772.3486725
If we subtract 2825 from 3200, we get 375.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3750, and continue the process.

Step 16:
If we divide 3750 by 565, we get 6 and a remainder of 360.
Write down 6 as next digit of the result. 
Result so far: 29772.34867256
If we take 3390 away from 3750, we end up with 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3600, and continue the process.

The quotient of the division is 29772.34867256, and the remainder is 3.6e-07.