We're dividing 257135 by 77 
We're looking to find how many times 77 goes into 257135.

On to step 1:
If we divide 2 by 77, we get 0 and a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 77

Advancing to step 2:
The number 77 fits into 25 0 times, leaving a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 25 after subtracting 0 from 25.
Bring next digit (7) of the dividend behind the 25 and repeat the process: 257 / 77

On to step 3:
77 goes into 257 3 times with a remainder of 26.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 231 from 257 and we're left with 26.
Bring next digit (1) of the dividend behind the 26 and repeat the process: 261 / 77

Let's proceed to step 4:
261 divided by 77 is 3 with a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 33.0
The remainder is 30 after subtracting 231 from 261.
Append the next digit (3) from the dividend to 30 and continue with: 303 / 77

Let's proceed to step 5:
The number 77 fits into 303 3 times, leaving a remainder of 72.
Put 3 as the next digit of the answer. 
Result so far: 333.0
If we take 231 away from 303, we end up with 72.
Include the next digit (5) from the dividend after 72, then repeat: 725 / 77

Let's proceed to step 6:
77 goes into 725 9 times with a remainder of 32.
The number 9 becomes the next digit in our result. 
Result so far: 3339.0
Subtract 693 from 725 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 7:
When dividing 320 by 77, we get 4 with a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 3339.4
Deduct 308 from 320 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
77 goes into 120 1 times with a remainder of 43.
The next digit of our result is 1. 
Result so far: 3339.41
Deduct 77 from 120 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Let's proceed to step 9:
77 can be fit into 430 5 times, resulting in a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 3339.415
If we subtract 385 from 430, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 10:
77 goes into 450 5 times with a remainder of 65.
Record the quotient 5 as the next digit in the result. 
Result so far: 3339.4155
The remainder is 65 after subtracting 385 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The final result is 3339.4155 with a remainder of 0.00065.