257584 divided by 42 
We're looking to find how many times 42 goes into 257584.

On to step 1:
42 can be fit into 2 0 times, resulting in a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 42

On 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
Deduct 0 from 25 and we're left with 25.
Append the next digit (7) from the dividend to 25 and continue with: 257 / 42

Moving on to step 3:
42 can be fit into 257 6 times, resulting in a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 252 from 257 and we're left with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 42

Let's proceed to step 4:
42 goes into 55 1 times with a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 61.0
Subtract 42 from 55 to get 13.
Grab the next digit (8) from the dividend, add it to 13, then carry on: 138 / 42

Moving on to step 5:
42 goes into 138 3 times with a remainder of 12.
Use 3 as the next digit of our solution. 
Result so far: 613.0
The remainder is 12 after subtracting 126 from 138.
Bring next digit (4) of the dividend behind the 12 and repeat the process: 124 / 42

Advancing to step 6:
If we divide 124 by 42, we get 2 and a remainder of 40.
Write down 2 as next digit of the result. 
Result so far: 6132.0
Deduct 84 from 124 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.

Let's proceed to step 7:
42 can be fit into 400 9 times, resulting in a remainder of 22.
Record the quotient 9 as the next digit in the result. 
Result so far: 6132.9
If we take 378 away from 400, we end up 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.

Advancing to step 8:
When dividing 220 by 42, we get 5 with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 6132.95
Deduct 210 from 220 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.

Step 9:
42 can be fit into 100 2 times, resulting in a remainder of 16.
Write down 2 as next digit of the result. 
Result so far: 6132.952
If we take 84 away from 100, we end up 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 10:
42 goes into 160 3 times with a remainder of 34.
Put 3 as the next digit of the answer. 
Result so far: 6132.9523
Deduct 126 from 160 and we're left with 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 11:
42 goes into 340 8 times with a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 6132.95238
If we take 336 away from 340, we end up 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 12:
40 divided by 42 is 0 with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 6132.95238
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 13:
400 divided by 42 is 9 with a remainder of 22.
Write down 9 as next digit of the result. 
Result so far: 6132.9523809
If we subtract 378 from 400, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 14:
The number 42 fits into 220 5 times, leaving a remainder of 10.
The next digit of our result is 5. 
Result so far: 6132.95238095
If we take 210 away from 220, we end up 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.

In conclusion, the division gives 6132.95238095 with a balance of 1e-08.