91114 divided by 16 
Our goal is to divide 91114 by 16.

Let's proceed to step 1:
9 divided by 16 is 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Fetch the next digit (1) from the dividend, attach it to 9 and continue: 91 / 16

Going ahead to step 2:
16 can be fit into 91 5 times, resulting in a remainder of 11.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 80 from 91 to get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 16

On to step 3:
The number 16 fits into 111 6 times, leaving a remainder of 15.
Write down 6 as next digit of the result. 
Result so far: 56.0
If we take 96 away from 111, we end up with 15.
Grab the next digit (1) from the dividend, add it to 15, then carry on: 151 / 16

Advancing to step 4:
16 can be fit into 151 9 times, resulting in a remainder of 7.
Use 9 as the next digit of our solution. 
Result so far: 569.0
If we subtract 144 from 151, we get 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 16

Let's proceed to step 5:
74 divided by 16 is 4 with a remainder of 10.
The next digit of our result is 4. 
Result so far: 5694.0
If we take 64 away from 74, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 6:
100 divided by 16 is 6 with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 5694.6
If we subtract 96 from 100, we get 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 7:
If we divide 40 by 16, we get 2 and a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 5694.62
If we subtract 32 from 40, 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 8:
16 goes into 80 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 5694.625
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.

Advancing to step 9:
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: 5694.625
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.

Moving 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: 5694.625
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.

The quotient of the division is 5694.625, and the remainder is 0.0.