345969 ÷ 31 
We're looking to find how many times 31 goes into 345969.

Step 1:
31 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 31

Let's proceed to step 2:
If we divide 34 by 31, we get 1 and a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 31 from 34 leaves us with 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 31

Advancing to step 3:
If we divide 35 by 31, we get 1 and a remainder of 4.
The next digit of our result is 1. 
Result so far: 11.0
If we take 31 away from 35, we end up with 4.
Include the next digit (9) from the dividend after 4, then repeat: 49 / 31

Moving on to step 4:
31 can be fit into 49 1 times, resulting in a remainder of 18.
The number 1 becomes the next digit in our result. 
Result so far: 111.0
Subtract 31 from 49 to get 18.
Fetch the next digit (6) from the dividend, attach it to 18 and continue: 186 / 31

Step 5:
The number 31 fits into 186 6 times, leaving a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 1116.0
Deduct 186 from 186 and we're left with 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 31

Let's proceed to step 6:
If we divide 9 by 31, we get 0 and a remainder of 9.
Put 0 as the next digit of the answer. 
Result so far: 11160.0
Deduct 0 from 9 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 7:
90 divided by 31 is 2 with a remainder of 28.
Use 2 as the next digit of our solution. 
Result so far: 11160.2
If we subtract 62 from 90, we get 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 8:
If we divide 280 by 31, we get 9 and a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 11160.29
If we take 279 away from 280, we end up 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.

Step 9:
31 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 11160.29
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 10:
The number 31 fits into 100 3 times, leaving a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 11160.2903
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.

On to step 11:
70 divided by 31 is 2 with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 11160.29032
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.

Advancing to step 12:
31 can be fit into 80 2 times, resulting in a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 11160.290322
Subtracting 62 from 80 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

In conclusion, the division gives 11160.290322 with a balance of 1.8e-06.