Let's divide 3697 by 25
We want to figure out the number of times 3697 can be divided by 25.

Going ahead to step 1:
If we divide 3 by 25, we get 0 and a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 25

Moving on to step 2:
When dividing 36 by 25, we get 1 with a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 25 from 36 and we're left with 11.
Grab the next digit (9) from the dividend, add it to 11, then carry on: 119 / 25

Moving on to step 3:
The number 25 fits into 119 4 times, leaving a remainder of 19.
Write down 4 as next digit of the result. 
Result so far: 14.0
Deduct 100 from 119 and we're left with 19.
Grab the next digit (7) from the dividend, add it to 19, then carry on: 197 / 25

Let's proceed to step 4:
25 can be fit into 197 7 times, resulting in a remainder of 22.
The number 7 becomes the next digit in our result. 
Result so far: 147.0
Subtracting 175 from 197 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 5:
When dividing 220 by 25, we get 8 with a remainder of 20.
The next digit of our result is 8. 
Result so far: 147.8
Subtracting 200 from 220 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 6:
The number 25 fits into 200 8 times, leaving a remainder of 0.
The next digit of our result is 8. 
Result so far: 147.88
The remainder is 0 after subtracting 200 from 200.
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 147.88 and a remainder of 0.0.