We look at the division of 677376 by 11 
Our goal is to divide 677376 by 11.

Let's proceed to step 1:
If we divide 6 by 11, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 11

On to step 2:
When dividing 67 by 11, we get 6 with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 6.0
The remainder is 1 after subtracting 66 from 67.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 11

On to step 3:
The number 11 fits into 17 1 times, leaving a remainder of 6.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
Subtract 11 from 17 to get 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 11

Advancing to step 4:
11 can be fit into 63 5 times, resulting in a remainder of 8.
The number 5 becomes the next digit in our result. 
Result so far: 615.0
The remainder is 8 after subtracting 55 from 63.
Append the next digit (7) from the dividend to 8 and continue with: 87 / 11

Moving on to step 5:
87 divided by 11 is 7 with a remainder of 10.
Record the quotient 7 as the next digit in the result. 
Result so far: 6157.0
Subtract 77 from 87 to get 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 11

Moving on to step 6:
11 can be fit into 106 9 times, resulting in a remainder of 7.
The next digit of our result is 9. 
Result so far: 61579.0
If we subtract 99 from 106, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
When dividing 70 by 11, we get 6 with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 61579.6
Subtracting 66 from 70 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
If we divide 40 by 11, we get 3 and a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 61579.63
Subtracting 33 from 40 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
11 goes into 70 6 times with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 61579.636
Subtracting 66 from 70 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 10:
11 can be fit into 40 3 times, resulting in a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 61579.6363
Deduct 33 from 40 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 11:
If we divide 70 by 11, we get 6 and a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 61579.63636
Deduct 66 from 70 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 12:
11 can be fit into 40 3 times, resulting in a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 61579.636363
Subtract 33 from 40 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 13:
11 can be fit into 70 6 times, resulting in a remainder of 4.
The next digit of our result is 6. 
Result so far: 61579.6363636
If we subtract 66 from 70, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 14:
11 can be fit into 40 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 61579.63636363
If we subtract 33 from 40, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Our division results in 61579.63636363 with a remaining 7e-09.