We're dividing 122565 by 16 
We want to figure out the number of times 122565 can be divided by 16.

On to step 1:
When dividing 1 by 16, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 16

Advancing to step 2:
16 goes into 12 0 times with a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Bring next digit (2) of the dividend behind the 12 and repeat the process: 122 / 16

On to step 3:
16 goes into 122 7 times with a remainder of 10.
The next digit of our result is 7. 
Result so far: 7.0
Subtracting 112 from 122 leaves us with 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 16

Moving on to step 4:
16 can be fit into 105 6 times, resulting in a remainder of 9.
Record the quotient 6 as the next digit in the result. 
Result so far: 76.0
Subtract 96 from 105 to get 9.
Fetch the next digit (6) from the dividend, attach it to 9 and continue: 96 / 16

Going ahead to step 5:
16 goes into 96 6 times with a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 766.0
The remainder is 0 after subtracting 96 from 96.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 16

Moving on to step 6:
When dividing 5 by 16, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 7660.0
If we subtract 0 from 5, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
16 goes into 50 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 7660.3
If we subtract 48 from 50, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
16 can be fit into 20 1 times, resulting in a remainder of 4.
The next digit of our result is 1. 
Result so far: 7660.31
If we subtract 16 from 20, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
The number 16 fits into 40 2 times, leaving a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 7660.312
Subtracting 32 from 40 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 10:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 7660.3125
If we take 80 away from 80, 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.

Step 11:
If we divide 0 by 16, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 7660.3125
Subtract 0 from 0 to 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.

On to step 12:
If we divide 0 by 16, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 7660.3125
The remainder is 0 after subtracting 0 from 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 7660.3125 and a remainder of 0.0.