419640 ÷ 25 
We're looking to find how many times 25 goes into 419640.

Moving on to step 1:
25 can be fit into 4 0 times, resulting in a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 25

On to step 2:
25 goes into 41 1 times with a remainder of 16.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 25 from 41 and we're left with 16.
Include the next digit (9) from the dividend after 16, then repeat: 169 / 25

Going ahead to step 3:
169 divided by 25 is 6 with a remainder of 19.
Write down 6 as next digit of the result. 
Result so far: 16.0
Subtract 150 from 169 to get 19.
Include the next digit (6) from the dividend after 19, then repeat: 196 / 25

Going ahead to step 4:
When dividing 196 by 25, we get 7 with a remainder of 21.
Write down 7 as next digit of the result. 
Result so far: 167.0
If we subtract 175 from 196, we get 21.
Fetch the next digit (4) from the dividend, attach it to 21 and continue: 214 / 25

Let's proceed to step 5:
The number 25 fits into 214 8 times, leaving a remainder of 14.
Use 8 as the next digit of our solution. 
Result so far: 1678.0
If we take 200 away from 214, we end up with 14.
Append the next digit (0) from the dividend to 14 and continue with: 140 / 25

Moving on to step 6:
The number 25 fits into 140 5 times, leaving a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 16785.0
Subtracting 125 from 140 leaves us 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.

Advancing to step 7:
25 can be fit into 150 6 times, resulting in a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 16785.6
Deduct 150 from 150 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.

Moving on to step 8:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 16785.6
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.

On to step 9:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 16785.6
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.

Our division results in 16785.6 with a remaining 0.0.