668739 ÷ 31 
We're looking to find how many times 31 goes into 668739.

Going ahead to step 1:
If we divide 6 by 31, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 31

On to step 2:
If we divide 66 by 31, we get 2 and a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 62 from 66 leaves us with 4.
Include the next digit (8) from the dividend after 4, then repeat: 48 / 31

Step 3:
31 goes into 48 1 times with a remainder of 17.
The next digit of our result is 1. 
Result so far: 21.0
Deduct 31 from 48 and we're left with 17.
Take the next digit (7) from the dividend and append it to 17, then repeat: 177 / 31

Advancing to step 4:
177 divided by 31 is 5 with a remainder of 22.
Write down 5 as next digit of the result. 
Result so far: 215.0
Subtract 155 from 177 to get 22.
Grab the next digit (3) from the dividend, add it to 22, then carry on: 223 / 31

Moving on to step 5:
The number 31 fits into 223 7 times, leaving a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 2157.0
Deduct 217 from 223 and we're left with 6.
Grab the next digit (9) from the dividend, add it to 6, then carry on: 69 / 31

Step 6:
31 can be fit into 69 2 times, resulting in a remainder of 7.
Record the quotient 2 as the next digit in the result. 
Result so far: 21572.0
The remainder is 7 after subtracting 62 from 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
If we divide 70 by 31, we get 2 and a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 21572.2
Subtract 62 from 70 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 8:
31 can be fit into 80 2 times, resulting in a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 21572.22
The remainder is 18 after subtracting 62 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

The final result is 21572.22 with a remainder of 0.018.