680635 ÷ 7 
We want to figure out the number of times 680635 can be divided by 7.

Going ahead to step 1:
When dividing 6 by 7, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 7

Moving on to step 2:
When dividing 68 by 7, we get 9 with a remainder of 5.
Write down 9 as next digit of the result. 
Result so far: 9.0
Deduct 63 from 68 and we're left with 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 7

Let's proceed to step 3:
If we divide 50 by 7, we get 7 and a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 97.0
If we take 49 away from 50, we end up with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 7

Going ahead to step 4:
If we divide 16 by 7, we get 2 and a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 972.0
If we take 14 away from 16, we end up with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 7

On to step 5:
7 goes into 23 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 9723.0
Deduct 21 from 23 and we're left with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 7

Step 6:
When dividing 25 by 7, we get 3 with a remainder of 4.
Write down 3 as next digit of the result. 
Result so far: 97233.0
Subtracting 21 from 25 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.

On to step 7:
If we divide 40 by 7, we get 5 and a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 97233.5
Subtract 35 from 40 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
When dividing 50 by 7, we get 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 97233.57
Subtract 49 from 50 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 9:
7 can be fit into 10 1 times, resulting in a remainder of 3.
The next digit of our result is 1. 
Result so far: 97233.571
If we subtract 7 from 10, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 10:
If we divide 30 by 7, we get 4 and a remainder of 2.
The next digit of our result is 4. 
Result so far: 97233.5714
The remainder is 2 after subtracting 28 from 30.
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 11:
When dividing 20 by 7, we get 2 with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 97233.57142
Deduct 14 from 20 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 12:
When dividing 60 by 7, we get 8 with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 97233.571428
The remainder is 4 after subtracting 56 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
The number 7 fits into 40 5 times, leaving a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 97233.5714285
Subtract 35 from 40 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 14:
7 can be fit into 50 7 times, resulting in a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 97233.57142857
Deduct 49 from 50 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 97233.57142857 and a remainder of 1e-09.