Let's divide 105937 by 45
We're looking to find how many times 45 goes into 105937.

Step 1:
If we divide 1 by 45, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 45

Let's proceed to step 2:
The number 45 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 45

Going ahead to step 3:
When dividing 105 by 45, we get 2 with a remainder of 15.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 90 from 105 and we're left with 15.
Grab the next digit (9) from the dividend, add it to 15, then carry on: 159 / 45

On to step 4:
45 goes into 159 3 times with a remainder of 24.
The number 3 becomes the next digit in our result. 
Result so far: 23.0
Subtracting 135 from 159 leaves us with 24.
Grab the next digit (3) from the dividend, add it to 24, then carry on: 243 / 45

Moving on to step 5:
45 goes into 243 5 times with a remainder of 18.
The number 5 becomes the next digit in our result. 
Result so far: 235.0
If we take 225 away from 243, we end up with 18.
Grab the next digit (7) from the dividend, add it to 18, then carry on: 187 / 45

Let's proceed to step 6:
187 divided by 45 is 4 with a remainder of 7.
The next digit of our result is 4. 
Result so far: 2354.0
If we subtract 180 from 187, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
When dividing 70 by 45, we get 1 with a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 2354.1
Subtract 45 from 70 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 8:
If we divide 250 by 45, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 2354.15
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 9:
250 divided by 45 is 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 2354.155
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 2354.155 with a balance of 0.0025.