We divide 102766 by 16
Let's see how many times 16 fits into 102766.

On to step 1:
16 can be fit into 1 0 times, resulting in a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 16

Advancing to step 2:
If we divide 10 by 16, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 16

Going ahead to step 3:
The number 16 fits into 102 6 times, leaving a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we subtract 96 from 102, we get 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 16

Advancing to step 4:
16 can be fit into 67 4 times, resulting in a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 64.0
Subtract 64 from 67 to get 3.
Include the next digit (6) from the dividend after 3, then repeat: 36 / 16

Moving on to step 5:
When dividing 36 by 16, we get 2 with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 642.0
If we take 32 away from 36, we end up with 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 16

On to step 6:
16 goes into 46 2 times with a remainder of 14.
Put 2 as the next digit of the answer. 
Result so far: 6422.0
The remainder is 14 after subtracting 32 from 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 7:
The number 16 fits into 140 8 times, leaving a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 6422.8
Subtract 128 from 140 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
The number 16 fits into 120 7 times, leaving a remainder of 8.
Write down 7 as next digit of the result. 
Result so far: 6422.87
If we subtract 112 from 120, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
80 divided by 16 is 5 with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 6422.875
The remainder is 0 after subtracting 80 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 10:
If we divide 0 by 16, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 6422.875
Deduct 0 from 0 and we're left 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:
The number 16 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 6422.875
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.

The quotient of the division is 6422.875, and the remainder is 0.0.