We look at the division of 177770 by 565 
We want to divide 177770 by 565.

Moving on to step 1:
If we divide 1 by 565, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 565

Step 2:
17 divided by 565 is 0 with a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Fetch the next digit (7) from the dividend, attach it to 17 and continue: 177 / 565

Step 3:
If we divide 177 by 565, we get 0 and a remainder of 177.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 177 and we're left with 177.
Take the next digit (7) from the dividend and append it to 177, then repeat: 1777 / 565

Advancing to step 4:
1777 divided by 565 is 3 with a remainder of 82.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we take 1695 away from 1777, we end up with 82.
Fetch the next digit (7) from the dividend, attach it to 82 and continue: 827 / 565

Going ahead to step 5:
565 goes into 827 1 times with a remainder of 262.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
Deduct 565 from 827 and we're left with 262.
Grab the next digit (0) from the dividend, add it to 262, then carry on: 2620 / 565

Let's proceed to step 6:
565 can be fit into 2620 4 times, resulting in a remainder of 360.
The number 4 becomes the next digit in our result. 
Result so far: 314.0
Deduct 2260 from 2620 and we're left with 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3600, and continue the process.

Let's proceed to step 7:
565 goes into 3600 6 times with a remainder of 210.
Write down 6 as next digit of the result. 
Result so far: 314.6
If we subtract 3390 from 3600, we get 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2100, and continue the process.

On to step 8:
When dividing 2100 by 565, we get 3 with a remainder of 405.
Put 3 as the next digit of the answer. 
Result so far: 314.63
Subtract 1695 from 2100 to get 405.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4050, and continue the process.

Step 9:
565 goes into 4050 7 times with a remainder of 95.
Put 7 as the next digit of the answer. 
Result so far: 314.637
Subtract 3955 from 4050 to get 95.
Since there are no more digits in the dividend, we add a zero to the remainder making it 950, and continue the process.

Moving on to step 10:
If we divide 950 by 565, we get 1 and a remainder of 385.
Put 1 as the next digit of the answer. 
Result so far: 314.6371
Deduct 565 from 950 and we're left with 385.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3850, and continue the process.

Advancing to step 11:
When dividing 3850 by 565, we get 6 with a remainder of 460.
Use 6 as the next digit of our solution. 
Result so far: 314.63716
The remainder is 460 after subtracting 3390 from 3850.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4600, and continue the process.

Step 12:
The number 565 fits into 4600 8 times, leaving a remainder of 80.
Put 8 as the next digit of the answer. 
Result so far: 314.637168
Subtracting 4520 from 4600 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

On to step 13:
800 divided by 565 is 1 with a remainder of 235.
Write down 1 as next digit of the result. 
Result so far: 314.6371681
Subtracting 565 from 800 leaves us with 235.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2350, and continue the process.

Let's proceed to step 14:
When dividing 2350 by 565, we get 4 with a remainder of 90.
Use 4 as the next digit of our solution. 
Result so far: 314.63716814
If we take 2260 away from 2350, we end up with 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

In conclusion, the division gives 314.63716814 with a balance of 9e-08.