25663 ÷ 42 
We want to figure out the number of times 25663 can be divided by 42.

Let's proceed to step 1:
If we divide 2 by 42, we get 0 and a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 42

Going ahead to step 2:
The number 42 fits into 25 0 times, leaving a remainder of 25.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Grab the next digit (6) from the dividend, add it to 25, then carry on: 256 / 42

Moving on to step 3:
42 goes into 256 6 times with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 252 from 256 and we're left with 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 42

Going ahead to step 4:
The number 42 fits into 46 1 times, leaving a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
The remainder is 4 after subtracting 42 from 46.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 42

Step 5:
43 divided by 42 is 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 611.0
If we take 42 away from 43, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 6:
The number 42 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 611.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 7:
42 can be fit into 100 2 times, resulting in a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 611.02
Deduct 84 from 100 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 8:
160 divided by 42 is 3 with a remainder of 34.
Use 3 as the next digit of our solution. 
Result so far: 611.023
Subtract 126 from 160 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 9:
42 goes into 340 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 611.0238
Deduct 336 from 340 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 10:
When dividing 40 by 42, we get 0 with a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 611.0238
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 11:
400 divided by 42 is 9 with a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 611.023809
The remainder is 22 after subtracting 378 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 12:
220 divided by 42 is 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 611.0238095
If we subtract 210 from 220, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 13:
When dividing 100 by 42, we get 2 with a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 611.02380952
The remainder is 16 after subtracting 84 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final outcome is 611.02380952, with a leftover of 1.6e-08.