We divide 580684 by 60
We want to figure out the number of times 580684 can be divided by 60.

On to step 1:
When dividing 5 by 60, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 60

Advancing to step 2:
60 goes into 58 0 times with a remainder of 58.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 58 to get 58.
Take the next digit (0) from the dividend and append it to 58, then repeat: 580 / 60

Step 3:
60 goes into 580 9 times with a remainder of 40.
The next digit of our result is 9. 
Result so far: 9.0
Subtract 540 from 580 to get 40.
Grab the next digit (6) from the dividend, add it to 40, then carry on: 406 / 60

Moving on to step 4:
60 can be fit into 406 6 times, resulting in a remainder of 46.
Use 6 as the next digit of our solution. 
Result so far: 96.0
Subtracting 360 from 406 leaves us with 46.
Grab the next digit (8) from the dividend, add it to 46, then carry on: 468 / 60

Moving on to step 5:
60 goes into 468 7 times with a remainder of 48.
Put 7 as the next digit of the answer. 
Result so far: 967.0
The remainder is 48 after subtracting 420 from 468.
Take the next digit (4) from the dividend and append it to 48, then repeat: 484 / 60

Advancing to step 6:
If we divide 484 by 60, we get 8 and a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 9678.0
Subtract 480 from 484 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
When dividing 40 by 60, we get 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 9678.0
Subtract 0 from 40 to 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.

Let's proceed to step 8:
When dividing 400 by 60, we get 6 with a remainder of 40.
The number 6 becomes the next digit in our result. 
Result so far: 9678.06
If we subtract 360 from 400, 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.

Step 9:
60 can be fit into 400 6 times, resulting in a remainder of 40.
Record the quotient 6 as the next digit in the result. 
Result so far: 9678.066
Deduct 360 from 400 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 9678.066, and the remainder is 0.004.