10905377 ÷ 261 
The aim is to understand the frequency of 261 in 10905377.

Advancing to step 1:
When dividing 1 by 261, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 261

Moving on to step 2:
10 divided by 261 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 261

Let's proceed to step 3:
109 divided by 261 is 0 with a remainder of 109.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 109, we end up with 109.
Include the next digit (0) from the dividend after 109, then repeat: 1090 / 261

Going ahead to step 4:
The number 261 fits into 1090 4 times, leaving a remainder of 46.
Write down 4 as next digit of the result. 
Result so far: 4.0
If we subtract 1044 from 1090, we get 46.
Fetch the next digit (5) from the dividend, attach it to 46 and continue: 465 / 261

On to step 5:
465 divided by 261 is 1 with a remainder of 204.
Record the quotient 1 as the next digit in the result. 
Result so far: 41.0
The remainder is 204 after subtracting 261 from 465.
Grab the next digit (3) from the dividend, add it to 204, then carry on: 2043 / 261

Let's proceed to step 6:
The number 261 fits into 2043 7 times, leaving a remainder of 216.
The number 7 becomes the next digit in our result. 
Result so far: 417.0
If we take 1827 away from 2043, we end up with 216.
Take the next digit (7) from the dividend and append it to 216, then repeat: 2167 / 261

Going ahead to step 7:
When dividing 2167 by 261, we get 8 with a remainder of 79.
Put 8 as the next digit of the answer. 
Result so far: 4178.0
If we take 2088 away from 2167, we end up with 79.
Fetch the next digit (7) from the dividend, attach it to 79 and continue: 797 / 261

Let's proceed to step 8:
If we divide 797 by 261, we get 3 and a remainder of 14.
Put 3 as the next digit of the answer. 
Result so far: 41783.0
The remainder is 14 after subtracting 783 from 797.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 9:
261 can be fit into 140 0 times, resulting in a remainder of 140.
Use 0 as the next digit of our solution. 
Result so far: 41783.0
Subtracting 0 from 140 leaves us with 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1400, and continue the process.

Going ahead to step 10:
If we divide 1400 by 261, we get 5 and a remainder of 95.
Write down 5 as next digit of the result. 
Result so far: 41783.05
The remainder is 95 after subtracting 1305 from 1400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 950, and continue the process.

Going ahead to step 11:
261 goes into 950 3 times with a remainder of 167.
Use 3 as the next digit of our solution. 
Result so far: 41783.053
Subtracting 783 from 950 leaves us with 167.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1670, and continue the process.

Let's proceed to step 12:
If we divide 1670 by 261, we get 6 and a remainder of 104.
Record the quotient 6 as the next digit in the result. 
Result so far: 41783.0536
Deduct 1566 from 1670 and we're left with 104.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1040, and continue the process.

Let's proceed to step 13:
261 goes into 1040 3 times with a remainder of 257.
Record the quotient 3 as the next digit in the result. 
Result so far: 41783.05363
If we take 783 away from 1040, we end up with 257.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2570, and continue the process.

Step 14:
2570 divided by 261 is 9 with a remainder of 221.
Write down 9 as next digit of the result. 
Result so far: 41783.053639
The remainder is 221 after subtracting 2349 from 2570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2210, and continue the process.

Going ahead to step 15:
2210 divided by 261 is 8 with a remainder of 122.
The number 8 becomes the next digit in our result. 
Result so far: 41783.0536398
If we subtract 2088 from 2210, we get 122.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1220, and continue the process.

On to step 16:
261 can be fit into 1220 4 times, resulting in a remainder of 176.
Record the quotient 4 as the next digit in the result. 
Result so far: 41783.05363984
Subtract 1044 from 1220 to get 176.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1760, and continue the process.

The final outcome is 41783.05363984, with a leftover of 1.76e-07.