We're dividing 71638 by 16 
Our goal is to divide 71638 by 16.

Let's proceed to step 1:
If we divide 7 by 16, we get 0 and a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Take the next digit (1) from the dividend and append it to 7, then repeat: 71 / 16

Step 2:
71 divided by 16 is 4 with a remainder of 7.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
If we subtract 64 from 71, we get 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 16

Advancing to step 3:
16 can be fit into 76 4 times, resulting in a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 44.0
The remainder is 12 after subtracting 64 from 76.
Append the next digit (3) from the dividend to 12 and continue with: 123 / 16

On to step 4:
16 can be fit into 123 7 times, resulting in a remainder of 11.
Write down 7 as next digit of the result. 
Result so far: 447.0
Subtracting 112 from 123 leaves us with 11.
Include the next digit (8) from the dividend after 11, then repeat: 118 / 16

Going ahead to step 5:
16 can be fit into 118 7 times, resulting in a remainder of 6.
The next digit of our result is 7. 
Result so far: 4477.0
Subtract 112 from 118 to 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.

Advancing to step 6:
16 can be fit into 60 3 times, resulting in a remainder of 12.
The next digit of our result is 3. 
Result so far: 4477.3
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.

On to step 7:
120 divided by 16 is 7 with a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 4477.37
If we take 112 away from 120, we end up 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.

Moving on to step 8:
16 can be fit into 80 5 times, resulting in a remainder of 0.
The next digit of our result is 5. 
Result so far: 4477.375
Deduct 80 from 80 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.

Advancing to step 9:
0 divided by 16 is 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 4477.375
If we take 0 away from 0, 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.

Going ahead to step 10:
When dividing 0 by 16, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 4477.375
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 4477.375, and the remainder is 0.0.