We're dividing 645669 by 11 
We're looking to find how many times 11 goes into 645669.

Going ahead to step 1:
11 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 11

On to step 2:
11 can be fit into 64 5 times, resulting in a remainder of 9.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 55 from 64, we get 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 11

Advancing to step 3:
If we divide 95 by 11, we get 8 and a remainder of 7.
The number 8 becomes the next digit in our result. 
Result so far: 58.0
If we take 88 away from 95, we end up with 7.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 11

Step 4:
11 goes into 76 6 times with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 586.0
Deduct 66 from 76 and we're left with 10.
Grab the next digit (6) from the dividend, add it to 10, then carry on: 106 / 11

Going ahead to step 5:
11 goes into 106 9 times with a remainder of 7.
Write down 9 as next digit of the result. 
Result so far: 5869.0
Subtract 99 from 106 to get 7.
Take the next digit (9) from the dividend and append it to 7, then repeat: 79 / 11

Going ahead to step 6:
79 divided by 11 is 7 with a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 58697.0
If we subtract 77 from 79, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
20 divided by 11 is 1 with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 58697.1
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 8:
When dividing 90 by 11, we get 8 with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 58697.18
The remainder is 2 after subtracting 88 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 9:
If we divide 20 by 11, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 58697.181
Subtract 11 from 20 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 10:
If we divide 90 by 11, we get 8 and a remainder of 2.
The next digit of our result is 8. 
Result so far: 58697.1818
If we subtract 88 from 90, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 11:
20 divided by 11 is 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 58697.18181
The remainder is 9 after subtracting 11 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 12:
If we divide 90 by 11, we get 8 and a remainder of 2.
The next digit of our result is 8. 
Result so far: 58697.181818
Subtract 88 from 90 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 13:
20 divided by 11 is 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 58697.1818181
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 14:
When dividing 90 by 11, we get 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 58697.18181818
The remainder is 2 after subtracting 88 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 58697.18181818 and a remainder of 2e-09.