We're dividing 677739 by 60 
We want to figure out the number of times 677739 can be divided by 60.

Advancing to step 1:
6 divided by 60 is 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 60

Going ahead to step 2:
If we divide 67 by 60, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 60 from 67, we get 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 60

Advancing to step 3:
When dividing 77 by 60, we get 1 with a remainder of 17.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Deduct 60 from 77 and we're left with 17.
Include the next digit (7) from the dividend after 17, then repeat: 177 / 60

Going ahead to step 4:
If we divide 177 by 60, we get 2 and a remainder of 57.
Record the quotient 2 as the next digit in the result. 
Result so far: 112.0
Deduct 120 from 177 and we're left with 57.
Take the next digit (3) from the dividend and append it to 57, then repeat: 573 / 60

Step 5:
573 divided by 60 is 9 with a remainder of 33.
The number 9 becomes the next digit in our result. 
Result so far: 1129.0
Subtract 540 from 573 to get 33.
Fetch the next digit (9) from the dividend, attach it to 33 and continue: 339 / 60

Let's proceed to step 6:
60 goes into 339 5 times with a remainder of 39.
Write down 5 as next digit of the result. 
Result so far: 11295.0
The remainder is 39 after subtracting 300 from 339.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 7:
60 can be fit into 390 6 times, resulting in a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 11295.6
Subtract 360 from 390 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
300 divided by 60 is 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 11295.65
The remainder is 0 after subtracting 300 from 300.
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:
60 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 11295.65
If we subtract 0 from 0, we 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.

Step 10:
60 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 11295.65
If we take 0 away from 0, we end up 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.

In conclusion, the division gives 11295.65 with a balance of 0.0.