686874 ÷ 21 
We're looking to find how many times 21 goes into 686874.

On to step 1:
When dividing 6 by 21, we get 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 21

Moving on to step 2:
The number 21 fits into 68 3 times, leaving a remainder of 5.
The next digit of our result is 3. 
Result so far: 3.0
Deduct 63 from 68 and we're left with 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 21

Going ahead to step 3:
56 divided by 21 is 2 with a remainder of 14.
Record the quotient 2 as the next digit in the result. 
Result so far: 32.0
If we subtract 42 from 56, we get 14.
Append the next digit (8) from the dividend to 14 and continue with: 148 / 21

Step 4:
21 goes into 148 7 times with a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 327.0
The remainder is 1 after subtracting 147 from 148.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 21

Moving on to step 5:
21 can be fit into 17 0 times, resulting in a remainder of 17.
The next digit of our result is 0. 
Result so far: 3270.0
The remainder is 17 after subtracting 0 from 17.
Bring next digit (4) of the dividend behind the 17 and repeat the process: 174 / 21

Advancing to step 6:
If we divide 174 by 21, we get 8 and a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 32708.0
Subtract 168 from 174 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 7:
21 can be fit into 60 2 times, resulting in a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 32708.2
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 8:
The number 21 fits into 180 8 times, leaving a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 32708.28
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
21 goes into 120 5 times with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 32708.285
Deduct 105 from 120 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 10:
If we divide 150 by 21, we get 7 and a remainder of 3.
The next digit of our result is 7. 
Result so far: 32708.2857
Subtract 147 from 150 to 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.

Moving on to step 11:
21 can be fit into 30 1 times, resulting in a remainder of 9.
The next digit of our result is 1. 
Result so far: 32708.28571
The remainder is 9 after subtracting 21 from 30.
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 12:
21 goes into 90 4 times with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 32708.285714
If we subtract 84 from 90, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 13:
60 divided by 21 is 2 with a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 32708.2857142
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 14:
The number 21 fits into 180 8 times, leaving a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 32708.28571428
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 32708.28571428 with a remainder of 1.2e-08.