We're dividing 914642 by 25 
Our goal is to divide 914642 by 25.

Step 1:
If we divide 9 by 25, we get 0 and a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Include the next digit (1) from the dividend after 9, then repeat: 91 / 25

Moving on to step 2:
The number 25 fits into 91 3 times, leaving a remainder of 16.
The next digit of our result is 3. 
Result so far: 3.0
Subtract 75 from 91 to get 16.
Include the next digit (4) from the dividend after 16, then repeat: 164 / 25

Step 3:
The number 25 fits into 164 6 times, leaving a remainder of 14.
Use 6 as the next digit of our solution. 
Result so far: 36.0
The remainder is 14 after subtracting 150 from 164.
Include the next digit (6) from the dividend after 14, then repeat: 146 / 25

Moving on to step 4:
25 can be fit into 146 5 times, resulting in a remainder of 21.
Record the quotient 5 as the next digit in the result. 
Result so far: 365.0
Subtracting 125 from 146 leaves us with 21.
Append the next digit (4) from the dividend to 21 and continue with: 214 / 25

Advancing to step 5:
The number 25 fits into 214 8 times, leaving a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 3658.0
If we take 200 away from 214, we end up with 14.
Grab the next digit (2) from the dividend, add it to 14, then carry on: 142 / 25

Advancing to step 6:
142 divided by 25 is 5 with a remainder of 17.
Put 5 as the next digit of the answer. 
Result so far: 36585.0
Deduct 125 from 142 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
170 divided by 25 is 6 with a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 36585.6
Subtract 150 from 170 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
When dividing 200 by 25, we get 8 with a remainder of 0.
The number 8 becomes the next digit in our result. 
Result so far: 36585.68
Deduct 200 from 200 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 9:
25 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 36585.68
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.

Going ahead to step 10:
The number 25 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 36585.68
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 36585.68, and the remainder is 0.0.