We're dividing 659679 by 31 
Our goal is to divide 659679 by 31.

On to step 1:
6 divided by 31 is 0 with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (5) from the dividend after 6, then repeat: 65 / 31

Moving on to step 2:
If we divide 65 by 31, we get 2 and a remainder of 3.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 62 from 65, we get 3.
Append the next digit (9) from the dividend to 3 and continue with: 39 / 31

Going ahead to step 3:
The number 31 fits into 39 1 times, leaving a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 21.0
Deduct 31 from 39 and we're left with 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 31

Moving on to step 4:
When dividing 86 by 31, we get 2 with a remainder of 24.
The next digit of our result is 2. 
Result so far: 212.0
Subtract 62 from 86 to get 24.
Fetch the next digit (7) from the dividend, attach it to 24 and continue: 247 / 31

On to step 5:
247 divided by 31 is 7 with a remainder of 30.
Write down 7 as next digit of the result. 
Result so far: 2127.0
If we take 217 away from 247, we end up with 30.
Include the next digit (9) from the dividend after 30, then repeat: 309 / 31

Let's proceed to step 6:
31 goes into 309 9 times with a remainder of 30.
Record the quotient 9 as the next digit in the result. 
Result so far: 21279.0
The remainder is 30 after subtracting 279 from 309.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 7:
The number 31 fits into 300 9 times, leaving a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 21279.9
If we take 279 away from 300, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 8:
The number 31 fits into 210 6 times, leaving a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 21279.96
Subtracting 186 from 210 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 9:
If we divide 240 by 31, we get 7 and a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 21279.967
If we subtract 217 from 240, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 10:
When dividing 230 by 31, we get 7 with a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 21279.9677
Deduct 217 from 230 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final result is 21279.9677 with a remainder of 0.00013.