100949 ÷ 45 
Let's see how many times 45 fits into 100949.

Advancing to step 1:
45 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 45

Step 2:
10 divided by 45 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Include the next digit (0) from the dividend after 10, then repeat: 100 / 45

Advancing to step 3:
45 goes into 100 2 times with a remainder of 10.
The next digit of our result is 2. 
Result so far: 2.0
Deduct 90 from 100 and we're left with 10.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 45

Going ahead to step 4:
109 divided by 45 is 2 with a remainder of 19.
The next digit of our result is 2. 
Result so far: 22.0
If we take 90 away from 109, we end up with 19.
Bring next digit (4) of the dividend behind the 19 and repeat the process: 194 / 45

Step 5:
If we divide 194 by 45, we get 4 and a remainder of 14.
The number 4 becomes the next digit in our result. 
Result so far: 224.0
The remainder is 14 after subtracting 180 from 194.
Grab the next digit (9) from the dividend, add it to 14, then carry on: 149 / 45

Moving on to step 6:
If we divide 149 by 45, we get 3 and a remainder of 14.
Put 3 as the next digit of the answer. 
Result so far: 2243.0
Deduct 135 from 149 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
The number 45 fits into 140 3 times, leaving a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 2243.3
If we take 135 away from 140, we end up 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.

Let's proceed to step 8:
If we divide 50 by 45, we get 1 and a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 2243.31
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
The number 45 fits into 50 1 times, leaving a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 2243.311
Subtracting 45 from 50 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.

The quotient of the division is 2243.311, and the remainder is 0.0005.