105834 ÷ 31 
We want to figure out the number of times 105834 can be divided by 31.

Step 1:
31 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 31

Going ahead to step 2:
10 divided by 31 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 31

Going ahead to step 3:
105 divided by 31 is 3 with a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 93 from 105 and we're left with 12.
Grab the next digit (8) from the dividend, add it to 12, then carry on: 128 / 31

Moving on to step 4:
128 divided by 31 is 4 with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 34.0
If we subtract 124 from 128, we get 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 31

Step 5:
If we divide 43 by 31, we get 1 and a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 341.0
If we subtract 31 from 43, we get 12.
Take the next digit (4) from the dividend and append it to 12, then repeat: 124 / 31

On to step 6:
124 divided by 31 is 4 with a remainder of 0.
Use 4 as the next digit of our solution. 
Result so far: 3414.0
If we take 124 away from 124, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 7:
When dividing 0 by 31, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 3414.0
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
The number 31 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 3414.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 3414.0 with a remainder of 0.0.