We're dividing 12577 by 40 
We want to figure out the number of times 12577 can be divided by 40.

Step 1:
When dividing 1 by 40, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 40

Let's proceed to step 2:
The number 40 fits into 12 0 times, leaving a remainder of 12.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 12 and we're left with 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 40

Going ahead to step 3:
40 goes into 125 3 times with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 120 from 125, we get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 40

On to step 4:
40 can be fit into 57 1 times, resulting in a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 31.0
If we take 40 away from 57, we end up with 17.
Fetch the next digit (7) from the dividend, attach it to 17 and continue: 177 / 40

Let's proceed to step 5:
40 can be fit into 177 4 times, resulting in a remainder of 17.
Write down 4 as next digit of the result. 
Result so far: 314.0
Subtract 160 from 177 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 6:
170 divided by 40 is 4 with a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 314.4
The remainder is 10 after subtracting 160 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 7:
40 goes into 100 2 times with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 314.42
If we take 80 away from 100, 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.

Advancing to step 8:
200 divided by 40 is 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 314.425
Deduct 200 from 200 and we're left 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.

Step 9:
The number 40 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 314.425
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 10:
40 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 314.425
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.

Our division results in 314.425 with a remaining 0.0.