We're dividing 642557 by 25 
We want to figure out the number of times 642557 can be divided by 25.

Moving on to step 1:
When dividing 6 by 25, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 25

Moving on to step 2:
64 divided by 25 is 2 with a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 50 from 64, we get 14.
Include the next digit (2) from the dividend after 14, then repeat: 142 / 25

On to step 3:
If we divide 142 by 25, we get 5 and a remainder of 17.
Use 5 as the next digit of our solution. 
Result so far: 25.0
If we take 125 away from 142, we end up with 17.
Append the next digit (5) from the dividend to 17 and continue with: 175 / 25

Step 4:
When dividing 175 by 25, we get 7 with a remainder of 0.
Record the quotient 7 as the next digit in the result. 
Result so far: 257.0
Subtracting 175 from 175 leaves us with 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 25

Going ahead to step 5:
If we divide 5 by 25, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 2570.0
Subtracting 0 from 5 leaves us with 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 25

Step 6:
25 can be fit into 57 2 times, resulting in a remainder of 7.
Record the quotient 2 as the next digit in the result. 
Result so far: 25702.0
If we subtract 50 from 57, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 7:
70 divided by 25 is 2 with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 25702.2
Deduct 50 from 70 and we're left 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.

Step 8:
25 goes into 200 8 times with a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 25702.28
If we subtract 200 from 200, 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 9:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 25702.28
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.

Step 10:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 25702.28
The remainder is 0 after subtracting 0 from 0.
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 25702.28 and a remainder of 0.0.