We're dividing 561631 by 16 
We want to figure out the number of times 561631 can be divided by 16.

Advancing to step 1:
When dividing 5 by 16, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 16

Let's proceed to step 2:
The number 16 fits into 56 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Deduct 48 from 56 and we're left with 8.
Grab the next digit (1) from the dividend, add it to 8, then carry on: 81 / 16

On to step 3:
81 divided by 16 is 5 with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
Subtracting 80 from 81 leaves us with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 16

Advancing to step 4:
If we divide 16 by 16, we get 1 and a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 351.0
The remainder is 0 after subtracting 16 from 16.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 16

Going ahead to step 5:
3 divided by 16 is 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 3510.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 16

Step 6:
31 divided by 16 is 1 with a remainder of 15.
The next digit of our result is 1. 
Result so far: 35101.0
If we take 16 away from 31, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 7:
When dividing 150 by 16, we get 9 with a remainder of 6.
The number 9 becomes the next digit in our result. 
Result so far: 35101.9
Subtract 144 from 150 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.

Moving on to step 8:
If we divide 60 by 16, we get 3 and a remainder of 12.
The next digit of our result is 3. 
Result so far: 35101.93
If we take 48 away from 60, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 9:
16 goes into 120 7 times with a remainder of 8.
Use 7 as the next digit of our solution. 
Result so far: 35101.937
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.

Advancing to step 10:
16 goes into 80 5 times with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 35101.9375
Subtracting 80 from 80 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.

Advancing to step 11:
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: 35101.9375
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.

On to step 12:
0 divided by 16 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 35101.9375
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 35101.9375, and the remainder is 0.0.