We're dividing 677538 by 65 
We're looking to find how many times 65 goes into 677538.

Step 1:
If we divide 6 by 65, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 65

Going ahead to step 2:
When dividing 67 by 65, we get 1 with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 65 from 67, we get 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 65

Step 3:
If we divide 27 by 65, we get 0 and a remainder of 27.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we take 0 away from 27, we end up with 27.
Grab the next digit (5) from the dividend, add it to 27, then carry on: 275 / 65

Advancing to step 4:
The number 65 fits into 275 4 times, leaving a remainder of 15.
Use 4 as the next digit of our solution. 
Result so far: 104.0
Subtracting 260 from 275 leaves us with 15.
Bring next digit (3) of the dividend behind the 15 and repeat the process: 153 / 65

Step 5:
65 can be fit into 153 2 times, resulting in a remainder of 23.
Record the quotient 2 as the next digit in the result. 
Result so far: 1042.0
Deduct 130 from 153 and we're left with 23.
Bring next digit (8) of the dividend behind the 23 and repeat the process: 238 / 65

Moving on to step 6:
When dividing 238 by 65, we get 3 with a remainder of 43.
Record the quotient 3 as the next digit in the result. 
Result so far: 10423.0
The remainder is 43 after subtracting 195 from 238.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Step 7:
65 can be fit into 430 6 times, resulting in a remainder of 40.
Put 6 as the next digit of the answer. 
Result so far: 10423.6
If we subtract 390 from 430, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
If we divide 400 by 65, we get 6 and a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 10423.66
If we take 390 away from 400, 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.

The final outcome is 10423.66, with a leftover of 0.01.