97171 ÷ 45 
We want to figure out the number of times 97171 can be divided by 45.

Going ahead to step 1:
45 can be fit into 9 0 times, resulting in a remainder of 9.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 45

Going ahead to step 2:
If we divide 97 by 45, we get 2 and a remainder of 7.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
If we subtract 90 from 97, we get 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 45

On to step 3:
When dividing 71 by 45, we get 1 with a remainder of 26.
Put 1 as the next digit of the answer. 
Result so far: 21.0
If we take 45 away from 71, we end up with 26.
Grab the next digit (7) from the dividend, add it to 26, then carry on: 267 / 45

Moving on to step 4:
267 divided by 45 is 5 with a remainder of 42.
Record the quotient 5 as the next digit in the result. 
Result so far: 215.0
If we subtract 225 from 267, we get 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 45

Going ahead to step 5:
45 goes into 421 9 times with a remainder of 16.
The number 9 becomes the next digit in our result. 
Result so far: 2159.0
Subtracting 405 from 421 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 6:
The number 45 fits into 160 3 times, leaving a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 2159.3
If we take 135 away from 160, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 7:
If we divide 250 by 45, we get 5 and a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 2159.35
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 8:
45 can be fit into 250 5 times, resulting in a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 2159.355
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 2159.355, and the remainder is 0.0025.