691661 ÷ 6 
We want to figure out the number of times 691661 can be divided by 6.

Let's proceed to step 1:
When dividing 6 by 6, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 6

On to step 2:
If we divide 9 by 6, we get 1 and a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we subtract 6 from 9, we get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 6

Moving on to step 3:
If we divide 31 by 6, we get 5 and a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 115.0
If we subtract 30 from 31, we get 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 6

Let's proceed to step 4:
If we divide 16 by 6, we get 2 and a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 1152.0
Subtracting 12 from 16 leaves us with 4.
Include the next digit (6) from the dividend after 4, then repeat: 46 / 6

Let's proceed to step 5:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of the result. 
Result so far: 11527.0
The remainder is 4 after subtracting 42 from 46.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 6

Step 6:
The number 6 fits into 41 6 times, leaving a remainder of 5.
The next digit of our result is 6. 
Result so far: 115276.0
The remainder is 5 after subtracting 36 from 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 7:
The number 6 fits into 50 8 times, leaving a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 115276.8
Deduct 48 from 50 and we're left with 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 8:
If we divide 20 by 6, we get 3 and a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 115276.83
Subtract 18 from 20 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.

Moving on to step 9:
6 goes into 20 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 115276.833
Deduct 18 from 20 and we're left with 2.
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 115276.833 and a remainder of 0.0002.