66637 ÷ 16 
Our goal is to divide 66637 by 16.

Advancing to step 1:
16 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 16

Advancing to step 2:
16 goes into 66 4 times with a remainder of 2.
The next digit of our result is 4. 
Result so far: 4.0
If we subtract 64 from 66, we get 2.
Include the next digit (6) from the dividend after 2, then repeat: 26 / 16

On to step 3:
If we divide 26 by 16, we get 1 and a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 41.0
If we take 16 away from 26, we end up with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 16

Moving on to step 4:
When dividing 103 by 16, we get 6 with a remainder of 7.
The number 6 becomes the next digit in our result. 
Result so far: 416.0
Subtract 96 from 103 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 16

Going ahead to step 5:
77 divided by 16 is 4 with a remainder of 13.
Record the quotient 4 as the next digit in the result. 
Result so far: 4164.0
Subtract 64 from 77 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 6:
16 goes into 130 8 times with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 4164.8
Deduct 128 from 130 and we're left with 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 7:
16 can be fit into 20 1 times, resulting in a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 4164.81
Deduct 16 from 20 and we're left 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.

Moving on to step 8:
When dividing 40 by 16, we get 2 with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 4164.812
The remainder is 8 after subtracting 32 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 9:
80 divided by 16 is 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 4164.8125
If we subtract 80 from 80, 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.

On to step 10:
The number 16 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 4164.8125
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.

Let's proceed to step 11:
If we divide 0 by 16, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 4164.8125
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.

After the division, we end up with 4164.8125 and a remainder of 0.0.