We look at the division of 577676 by 45 
We want to figure out the number of times 577676 can be divided by 45.

Step 1:
45 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (7) from the dividend to 5 and continue with: 57 / 45

Moving on to step 2:
When dividing 57 by 45, we get 1 with a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 45 away from 57, we end up with 12.
Take the next digit (7) from the dividend and append it to 12, then repeat: 127 / 45

Advancing to step 3:
The number 45 fits into 127 2 times, leaving a remainder of 37.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we take 90 away from 127, we end up with 37.
Include the next digit (6) from the dividend after 37, then repeat: 376 / 45

Let's proceed to step 4:
When dividing 376 by 45, we get 8 with a remainder of 16.
The number 8 becomes the next digit in our result. 
Result so far: 128.0
Subtract 360 from 376 to get 16.
Grab the next digit (7) from the dividend, add it to 16, then carry on: 167 / 45

Moving on to step 5:
The number 45 fits into 167 3 times, leaving a remainder of 32.
Put 3 as the next digit of the answer. 
Result so far: 1283.0
Subtracting 135 from 167 leaves us with 32.
Bring next digit (6) of the dividend behind the 32 and repeat the process: 326 / 45

Let's proceed to step 6:
The number 45 fits into 326 7 times, leaving a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 12837.0
Subtract 315 from 326 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 7:
The number 45 fits into 110 2 times, leaving a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 12837.2
The remainder is 20 after subtracting 90 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
200 divided by 45 is 4 with a remainder of 20.
The number 4 becomes the next digit in our result. 
Result so far: 12837.24
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
45 goes into 200 4 times with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 12837.244
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

In conclusion, the division gives 12837.244 with a balance of 0.002.