We look at the division of 71421734 by 105 
We want to figure out the number of times 71421734 can be divided by 105.

Advancing to step 1:
The number 105 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 105

Moving on to step 2:
105 goes into 71 0 times with a remainder of 71.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 71 leaves us with 71.
Include the next digit (4) from the dividend after 71, then repeat: 714 / 105

Moving on to step 3:
When dividing 714 by 105, we get 6 with a remainder of 84.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 630 from 714 and we're left with 84.
Take the next digit (2) from the dividend and append it to 84, then repeat: 842 / 105

Advancing to step 4:
105 goes into 842 8 times with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 68.0
Subtract 840 from 842 to get 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 105

Step 5:
105 goes into 21 0 times with a remainder of 21.
Write down 0 as next digit of the result. 
Result so far: 680.0
Deduct 0 from 21 and we're left with 21.
Include the next digit (7) from the dividend after 21, then repeat: 217 / 105

On to step 6:
If we divide 217 by 105, we get 2 and a remainder of 7.
Put 2 as the next digit of the answer. 
Result so far: 6802.0
Subtract 210 from 217 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 105

Going ahead to step 7:
The number 105 fits into 73 0 times, leaving a remainder of 73.
Write down 0 as next digit of the result. 
Result so far: 68020.0
If we take 0 away from 73, we end up with 73.
Take the next digit (4) from the dividend and append it to 73, then repeat: 734 / 105

Moving on to step 8:
The number 105 fits into 734 6 times, leaving a remainder of 104.
The next digit of our result is 6. 
Result so far: 680206.0
Subtracting 630 from 734 leaves us with 104.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1040, and continue the process.

On to step 9:
105 can be fit into 1040 9 times, resulting in a remainder of 95.
Use 9 as the next digit of our solution. 
Result so far: 680206.9
Subtract 945 from 1040 to get 95.
Since there are no more digits in the dividend, we add a zero to the remainder making it 950, and continue the process.

Step 10:
If we divide 950 by 105, we get 9 and a remainder of 5.
Use 9 as the next digit of our solution. 
Result so far: 680206.99
Deduct 945 from 950 and we're left 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.

After the division, we end up with 680206.99 and a remainder of 0.005.