We look at the division of 44338 by 16 
Our goal is to divide 44338 by 16.

Let's proceed to step 1:
When dividing 4 by 16, we get 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 16

Advancing to step 2:
When dividing 44 by 16, we get 2 with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtract 32 from 44 to get 12.
Bring next digit (3) of the dividend behind the 12 and repeat the process: 123 / 16

Going ahead to step 3:
123 divided by 16 is 7 with a remainder of 11.
The next digit of our result is 7. 
Result so far: 27.0
If we take 112 away from 123, we end up with 11.
Take the next digit (3) from the dividend and append it to 11, then repeat: 113 / 16

Advancing to step 4:
113 divided by 16 is 7 with a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 277.0
Subtract 112 from 113 to get 1.
Take the next digit (8) from the dividend and append it to 1, then repeat: 18 / 16

Step 5:
If we divide 18 by 16, we get 1 and a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 2771.0
Subtract 16 from 18 to 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.

Going ahead to step 6:
When dividing 20 by 16, we get 1 with a remainder of 4.
The next digit of our result is 1. 
Result so far: 2771.1
Subtracting 16 from 20 leaves us with 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 7:
16 goes into 40 2 times with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 2771.12
Deduct 32 from 40 and we're left 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.

Let's proceed to step 8:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 2771.125
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.

Let's proceed to step 9:
0 divided by 16 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 2771.125
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 10:
The number 16 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 2771.125
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.

In conclusion, the division gives 2771.125 with a balance of 0.0.