We're dividing 25582842 by 338 
We want to figure out the number of times 25582842 can be divided by 338.

Going ahead to step 1:
338 can be fit into 2 0 times, resulting in a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 338

Let's proceed to step 2:
25 divided by 338 is 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Fetch the next digit (5) from the dividend, attach it to 25 and continue: 255 / 338

Going ahead to step 3:
338 can be fit into 255 0 times, resulting in a remainder of 255.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 255 and we're left with 255.
Include the next digit (8) from the dividend after 255, then repeat: 2558 / 338

Step 4:
2558 divided by 338 is 7 with a remainder of 192.
Put 7 as the next digit of the answer. 
Result so far: 7.0
If we take 2366 away from 2558, we end up with 192.
Include the next digit (2) from the dividend after 192, then repeat: 1922 / 338

Moving on to step 5:
The number 338 fits into 1922 5 times, leaving a remainder of 232.
Record the quotient 5 as the next digit in the result. 
Result so far: 75.0
Deduct 1690 from 1922 and we're left with 232.
Fetch the next digit (8) from the dividend, attach it to 232 and continue: 2328 / 338

Step 6:
The number 338 fits into 2328 6 times, leaving a remainder of 300.
Write down 6 as next digit of the result. 
Result so far: 756.0
Subtracting 2028 from 2328 leaves us with 300.
Fetch the next digit (4) from the dividend, attach it to 300 and continue: 3004 / 338

Advancing to step 7:
3004 divided by 338 is 8 with a remainder of 300.
Record the quotient 8 as the next digit in the result. 
Result so far: 7568.0
The remainder is 300 after subtracting 2704 from 3004.
Bring next digit (2) of the dividend behind the 300 and repeat the process: 3002 / 338

Moving on to step 8:
When dividing 3002 by 338, we get 8 with a remainder of 298.
The number 8 becomes the next digit in our result. 
Result so far: 75688.0
Subtracting 2704 from 3002 leaves us with 298.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2980, and continue the process.

Going ahead to step 9:
338 goes into 2980 8 times with a remainder of 276.
Use 8 as the next digit of our solution. 
Result so far: 75688.8
If we take 2704 away from 2980, we end up with 276.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2760, and continue the process.

Going ahead to step 10:
If we divide 2760 by 338, we get 8 and a remainder of 56.
Use 8 as the next digit of our solution. 
Result so far: 75688.88
If we take 2704 away from 2760, we end up with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

The quotient of the division is 75688.88, and the remainder is 0.056.