Let's divide 577667 by 45
We want to divide 577667 by 45.

On to step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 45

On to step 2:
57 divided by 45 is 1 with a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 45 from 57 and we're left with 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 45

Moving on to step 3:
45 can be fit into 127 2 times, resulting in a remainder of 37.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
If we subtract 90 from 127, we get 37.
Grab the next digit (6) from the dividend, add it to 37, then carry on: 376 / 45

Let's proceed to step 4:
45 goes into 376 8 times with a remainder of 16.
The number 8 becomes the next digit in our result. 
Result so far: 128.0
Deduct 360 from 376 and we're left with 16.
Bring next digit (6) of the dividend behind the 16 and repeat the process: 166 / 45

Step 5:
166 divided by 45 is 3 with a remainder of 31.
Use 3 as the next digit of our solution. 
Result so far: 1283.0
Subtract 135 from 166 to get 31.
Grab the next digit (7) from the dividend, add it to 31, then carry on: 317 / 45

Going ahead to step 6:
45 can be fit into 317 7 times, resulting in a remainder of 2.
The next digit of our result is 7. 
Result so far: 12837.0
The remainder is 2 after subtracting 315 from 317.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
The number 45 fits into 20 0 times, leaving a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 12837.0
Deduct 0 from 20 and we're left 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.

On to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
The next digit of our result is 4. 
Result so far: 12837.04
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.

Moving on to step 9:
The number 45 fits into 200 4 times, leaving a remainder of 20.
The number 4 becomes the next digit in our result. 
Result so far: 12837.044
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 12837.044 and a remainder of 0.002.