We're dividing 105031 by 22 
We're looking to find how many times 22 goes into 105031.

Going ahead to step 1:
When dividing 1 by 22, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 22

Step 2:
10 divided by 22 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 22

Let's proceed to step 3:
If we divide 105 by 22, we get 4 and a remainder of 17.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 88 away from 105, we end up with 17.
Take the next digit (0) from the dividend and append it to 17, then repeat: 170 / 22

Step 4:
22 goes into 170 7 times with a remainder of 16.
Use 7 as the next digit of our solution. 
Result so far: 47.0
Subtracting 154 from 170 leaves us with 16.
Append the next digit (3) from the dividend to 16 and continue with: 163 / 22

Step 5:
163 divided by 22 is 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 477.0
Subtracting 154 from 163 leaves us with 9.
Take the next digit (1) from the dividend and append it to 9, then repeat: 91 / 22

Step 6:
22 goes into 91 4 times with a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 4774.0
Subtracting 88 from 91 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
When dividing 30 by 22, we get 1 with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 4774.1
Subtract 22 from 30 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.

On to step 8:
80 divided by 22 is 3 with a remainder of 14.
Record the quotient 3 as the next digit in the result. 
Result so far: 4774.13
If we subtract 66 from 80, we get 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 9:
When dividing 140 by 22, we get 6 with a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 4774.136
The remainder is 8 after subtracting 132 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 10:
When dividing 80 by 22, we get 3 with a remainder of 14.
Put 3 as the next digit of the answer. 
Result so far: 4774.1363
Subtract 66 from 80 to get 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 11:
140 divided by 22 is 6 with a remainder of 8.
The next digit of our result is 6. 
Result so far: 4774.13636
If we subtract 132 from 140, we 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:
The number 22 fits into 80 3 times, leaving a remainder of 14.
Record the quotient 3 as the next digit in the result. 
Result so far: 4774.136363
If we subtract 66 from 80, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 13:
140 divided by 22 is 6 with a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 4774.1363636
Subtracting 132 from 140 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 14:
80 divided by 22 is 3 with a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 4774.13636363
Deduct 66 from 80 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.

The quotient of the division is 4774.13636363, and the remainder is 1.4e-08.