We're dividing 876938 by 65 
We want to divide 876938 by 65.

Let's proceed to step 1:
If we divide 8 by 65, we get 0 and a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 65

Advancing to step 2:
87 divided by 65 is 1 with a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 65 from 87 leaves us with 22.
Append the next digit (6) from the dividend to 22 and continue with: 226 / 65

Moving on to step 3:
If we divide 226 by 65, we get 3 and a remainder of 31.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 195 from 226, we get 31.
Fetch the next digit (9) from the dividend, attach it to 31 and continue: 319 / 65

Moving on to step 4:
When dividing 319 by 65, we get 4 with a remainder of 59.
Use 4 as the next digit of our solution. 
Result so far: 134.0
If we subtract 260 from 319, we get 59.
Append the next digit (3) from the dividend to 59 and continue with: 593 / 65

On to step 5:
65 can be fit into 593 9 times, resulting in a remainder of 8.
Use 9 as the next digit of our solution. 
Result so far: 1349.0
If we subtract 585 from 593, we get 8.
Fetch the next digit (8) from the dividend, attach it to 8 and continue: 88 / 65

Step 6:
65 can be fit into 88 1 times, resulting in a remainder of 23.
The number 1 becomes the next digit in our result. 
Result so far: 13491.0
Deduct 65 from 88 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
65 goes into 230 3 times with a remainder of 35.
Use 3 as the next digit of our solution. 
Result so far: 13491.3
If we subtract 195 from 230, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 8:
65 can be fit into 350 5 times, resulting in a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 13491.35
Subtract 325 from 350 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 9:
If we divide 250 by 65, we get 3 and a remainder of 55.
Use 3 as the next digit of our solution. 
Result so far: 13491.353
The remainder is 55 after subtracting 195 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 10:
The number 65 fits into 550 8 times, leaving a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 13491.3538
If we subtract 520 from 550, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 11:
If we divide 300 by 65, we get 4 and a remainder of 40.
Record the quotient 4 as the next digit in the result. 
Result so far: 13491.35384
Deduct 260 from 300 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 12:
65 can be fit into 400 6 times, resulting in a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 13491.353846
Deduct 390 from 400 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 13:
If we divide 100 by 65, we get 1 and a remainder of 35.
The next digit of our result is 1. 
Result so far: 13491.3538461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 14:
The number 65 fits into 350 5 times, leaving a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 13491.35384615
Subtract 325 from 350 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 13491.35384615 with a balance of 2.5e-08.