Let's divide 1634 by 25
Our goal is to divide 1634 by 25.

Advancing to step 1:
1 divided by 25 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 25

On to step 2:
The number 25 fits into 16 0 times, leaving a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 16, we end up with 16.
Grab the next digit (3) from the dividend, add it to 16, then carry on: 163 / 25

Let's proceed to step 3:
When dividing 163 by 25, we get 6 with a remainder of 13.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtract 150 from 163 to get 13.
Fetch the next digit (4) from the dividend, attach it to 13 and continue: 134 / 25

Going ahead to step 4:
25 goes into 134 5 times with a remainder of 9.
Use 5 as the next digit of our solution. 
Result so far: 65.0
Deduct 125 from 134 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 5:
90 divided by 25 is 3 with a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 65.3
Deduct 75 from 90 and we're left 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 6:
150 divided by 25 is 6 with a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 65.36
If we subtract 150 from 150, 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.

Let's proceed to step 7:
If we divide 0 by 25, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 65.36
Deduct 0 from 0 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 8:
When dividing 0 by 25, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 65.36
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 65.36, and the remainder is 0.0.