We look at the division of 505874 by 77 
Our goal is to divide 505874 by 77.

Advancing to step 1:
If we divide 5 by 77, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 77

Going ahead to step 2:
When dividing 50 by 77, we get 0 with a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 50 and we're left with 50.
Include the next digit (5) from the dividend after 50, then repeat: 505 / 77

On to step 3:
If we divide 505 by 77, we get 6 and a remainder of 43.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 462 from 505 and we're left with 43.
Fetch the next digit (8) from the dividend, attach it to 43 and continue: 438 / 77

Step 4:
77 can be fit into 438 5 times, resulting in a remainder of 53.
Put 5 as the next digit of the answer. 
Result so far: 65.0
Subtract 385 from 438 to get 53.
Take the next digit (7) from the dividend and append it to 53, then repeat: 537 / 77

Advancing to step 5:
77 goes into 537 6 times with a remainder of 75.
Write down 6 as next digit of the result. 
Result so far: 656.0
Subtracting 462 from 537 leaves us with 75.
Bring next digit (4) of the dividend behind the 75 and repeat the process: 754 / 77

Let's proceed to step 6:
If we divide 754 by 77, we get 9 and a remainder of 61.
The number 9 becomes the next digit in our result. 
Result so far: 6569.0
Subtract 693 from 754 to get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Let's proceed to step 7:
77 goes into 610 7 times with a remainder of 71.
The next digit of our result is 7. 
Result so far: 6569.7
Subtracting 539 from 610 leaves us with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Advancing to step 8:
77 can be fit into 710 9 times, resulting in a remainder of 17.
Record the quotient 9 as the next digit in the result. 
Result so far: 6569.79
Subtract 693 from 710 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 9:
If we divide 170 by 77, we get 2 and a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 6569.792
Deduct 154 from 170 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.

Moving on to step 10:
160 divided by 77 is 2 with a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 6569.7922
Deduct 154 from 160 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 6569.7922 and a remainder of 6e-05.