We divide 729 by 31
We want to figure out the number of times 729 can be divided by 31.

Going ahead to step 1:
7 divided by 31 is 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Bring next digit (2) of the dividend behind the 7 and repeat the process: 72 / 31

Moving on to step 2:
If we divide 72 by 31, we get 2 and a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Deduct 62 from 72 and we're left with 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 31

Advancing to step 3:
The number 31 fits into 109 3 times, leaving a remainder of 16.
Write down 3 as next digit of the result. 
Result so far: 23.0
Subtract 93 from 109 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 4:
The number 31 fits into 160 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 23.5
Subtracting 155 from 160 leaves us with 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 5:
31 can be fit into 50 1 times, resulting in a remainder of 19.
The next digit of our result is 1. 
Result so far: 23.51
Subtracting 31 from 50 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 6:
190 divided by 31 is 6 with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 23.516
If we take 186 away from 190, we end up 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.

Moving on to step 7:
When dividing 40 by 31, we get 1 with a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 23.5161
If we subtract 31 from 40, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 8:
31 goes into 90 2 times with a remainder of 28.
The next digit of our result is 2. 
Result so far: 23.51612
Subtracting 62 from 90 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 9:
280 divided by 31 is 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 23.516129
The remainder is 1 after subtracting 279 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 10:
10 divided by 31 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 23.516129
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 11:
31 goes into 100 3 times with a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 23.51612903
If we take 93 away from 100, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Our division results in 23.51612903 with a remaining 7e-09.