We look at the division of 838679 by 16 
We're looking to find how many times 16 goes into 838679.

Going ahead to step 1:
16 can be fit into 8 0 times, resulting in a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Include the next digit (3) from the dividend after 8, then repeat: 83 / 16

Moving on to step 2:
The number 16 fits into 83 5 times, leaving a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we take 80 away from 83, we end up with 3.
Include the next digit (8) from the dividend after 3, then repeat: 38 / 16

On to step 3:
The number 16 fits into 38 2 times, leaving a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 52.0
Deduct 32 from 38 and we're left with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 16

Moving on to step 4:
66 divided by 16 is 4 with a remainder of 2.
Put 4 as the next digit of the answer. 
Result so far: 524.0
The remainder is 2 after subtracting 64 from 66.
Include the next digit (7) from the dividend after 2, then repeat: 27 / 16

Let's proceed to step 5:
The number 16 fits into 27 1 times, leaving a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 5241.0
Subtract 16 from 27 to get 11.
Grab the next digit (9) from the dividend, add it to 11, then carry on: 119 / 16

Let's proceed to step 6:
16 goes into 119 7 times with a remainder of 7.
The next digit of our result is 7. 
Result so far: 52417.0
Subtract 112 from 119 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
16 can be fit into 70 4 times, resulting in a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 52417.4
If we subtract 64 from 70, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 8:
The number 16 fits into 60 3 times, leaving a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 52417.43
If we subtract 48 from 60, we 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 9:
When dividing 120 by 16, we get 7 with a remainder of 8.
Record the quotient 7 as the next digit in the result. 
Result so far: 52417.437
Subtract 112 from 120 to 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.

Let's proceed to step 10:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 52417.4375
Subtract 80 from 80 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 11:
16 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 52417.4375
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.

Moving on to step 12:
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: 52417.4375
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.

The quotient of the division is 52417.4375, and the remainder is 0.0.