We look at the division of 677305 by 4 
We're looking to find how many times 4 goes into 677305.

Going ahead to step 1:
When dividing 6 by 4, we get 1 with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 4 from 6, we get 2.
Include the next digit (7) from the dividend after 2, then repeat: 27 / 4

On to step 2:
The number 4 fits into 27 6 times, leaving a remainder of 3.
The next digit of our result is 6. 
Result so far: 16.0
Deduct 24 from 27 and we're left with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 4

Going ahead to step 3:
If we divide 37 by 4, we get 9 and a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 169.0
Subtracting 36 from 37 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 4:
4 goes into 13 3 times with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 1693.0
Subtracting 12 from 13 leaves us with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 4

On to step 5:
4 goes into 10 2 times with a remainder of 2.
The next digit of our result is 2. 
Result so far: 16932.0
If we take 8 away from 10, we end up with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 4

Step 6:
4 goes into 25 6 times with a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 169326.0
Subtracting 24 from 25 leaves us 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.

On to step 7:
The number 4 fits into 10 2 times, leaving a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 169326.2
The remainder is 2 after subtracting 8 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 8:
The number 4 fits into 20 5 times, leaving a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 169326.25
Subtracting 20 from 20 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 9:
The number 4 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 169326.25
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 10:
When dividing 0 by 4, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 169326.25
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 169326.25, and the remainder is 0.0.