We're dividing 8775842 by 634 
We want to divide 8775842 by 634.

Moving on to step 1:
When dividing 8 by 634, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 634

Moving on to step 2:
634 can be fit into 87 0 times, resulting in a remainder of 87.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 87, we get 87.
Fetch the next digit (7) from the dividend, attach it to 87 and continue: 877 / 634

Moving on to step 3:
634 can be fit into 877 1 times, resulting in a remainder of 243.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 634 from 877, we get 243.
Take the next digit (5) from the dividend and append it to 243, then repeat: 2435 / 634

Advancing to step 4:
2435 divided by 634 is 3 with a remainder of 533.
The next digit of our result is 3. 
Result so far: 13.0
Subtracting 1902 from 2435 leaves us with 533.
Take the next digit (8) from the dividend and append it to 533, then repeat: 5338 / 634

Going ahead to step 5:
5338 divided by 634 is 8 with a remainder of 266.
The number 8 becomes the next digit in our result. 
Result so far: 138.0
Deduct 5072 from 5338 and we're left with 266.
Fetch the next digit (4) from the dividend, attach it to 266 and continue: 2664 / 634

Let's proceed to step 6:
2664 divided by 634 is 4 with a remainder of 128.
The number 4 becomes the next digit in our result. 
Result so far: 1384.0
Deduct 2536 from 2664 and we're left with 128.
Fetch the next digit (2) from the dividend, attach it to 128 and continue: 1282 / 634

Let's proceed to step 7:
When dividing 1282 by 634, we get 2 with a remainder of 14.
The number 2 becomes the next digit in our result. 
Result so far: 13842.0
Subtracting 1268 from 1282 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 8:
When dividing 140 by 634, we get 0 with a remainder of 140.
The number 0 becomes the next digit in our result. 
Result so far: 13842.0
The remainder is 140 after subtracting 0 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1400, and continue the process.

On to step 9:
634 goes into 1400 2 times with a remainder of 132.
Write down 2 as next digit of the result. 
Result so far: 13842.02
The remainder is 132 after subtracting 1268 from 1400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1320, and continue the process.

Going ahead to step 10:
634 goes into 1320 2 times with a remainder of 52.
The number 2 becomes the next digit in our result. 
Result so far: 13842.022
Deduct 1268 from 1320 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

The quotient of the division is 13842.022, and the remainder is 0.0052.