We look at the division of 253862 by 2 
The aim is to understand the frequency of 2 in 253862.

Advancing to step 1:
2 divided by 2 is 1 with a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 2 from 2 to get 0.
Grab the next digit (5) from the dividend, add it to 0, then carry on: 5 / 2

Going ahead to step 2:
5 divided by 2 is 2 with a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we take 4 away from 5, we end up with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 2

Advancing to step 3:
2 goes into 13 6 times with a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 126.0
If we subtract 12 from 13, we get 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 2

Advancing to step 4:
When dividing 18 by 2, we get 9 with a remainder of 0.
Write down 9 as next digit of the result. 
Result so far: 1269.0
Subtract 18 from 18 to get 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 2

Advancing to step 5:
6 divided by 2 is 3 with a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 12693.0
Deduct 6 from 6 and we're left with 0.
Grab the next digit (2) from the dividend, add it to 0, then carry on: 2 / 2

Moving on to step 6:
When dividing 2 by 2, we get 1 with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 126931.0
If we take 2 away from 2, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
0 divided by 2 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 126931.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
If we divide 0 by 2, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 126931.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 126931.0 and a remainder of 0.0.