3434711 ÷ 126 
We're looking to find how many times 126 goes into 3434711.

Advancing to step 1:
If we divide 3 by 126, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 126

Let's proceed to step 2:
34 divided by 126 is 0 with a remainder of 34.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 34, we get 34.
Bring next digit (3) of the dividend behind the 34 and repeat the process: 343 / 126

Moving on to step 3:
The number 126 fits into 343 2 times, leaving a remainder of 91.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we subtract 252 from 343, we get 91.
Take the next digit (4) from the dividend and append it to 91, then repeat: 914 / 126

On to step 4:
914 divided by 126 is 7 with a remainder of 32.
The number 7 becomes the next digit in our result. 
Result so far: 27.0
The remainder is 32 after subtracting 882 from 914.
Bring next digit (7) of the dividend behind the 32 and repeat the process: 327 / 126

Advancing to step 5:
126 can be fit into 327 2 times, resulting in a remainder of 75.
Use 2 as the next digit of our solution. 
Result so far: 272.0
The remainder is 75 after subtracting 252 from 327.
Bring next digit (1) of the dividend behind the 75 and repeat the process: 751 / 126

Step 6:
The number 126 fits into 751 5 times, leaving a remainder of 121.
The next digit of our result is 5. 
Result so far: 2725.0
If we subtract 630 from 751, we get 121.
Bring next digit (1) of the dividend behind the 121 and repeat the process: 1211 / 126

Moving on to step 7:
If we divide 1211 by 126, we get 9 and a remainder of 77.
Put 9 as the next digit of the answer. 
Result so far: 27259.0
Deduct 1134 from 1211 and we're left with 77.
Since there are no more digits in the dividend, we add a zero to the remainder making it 770, and continue the process.

Moving on to step 8:
When dividing 770 by 126, we get 6 with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 27259.6
Subtract 756 from 770 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.

Going ahead to step 9:
126 can be fit into 140 1 times, resulting in a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 27259.61
Subtract 126 from 140 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.

Going ahead to step 10:
126 goes into 140 1 times with a remainder of 14.
The next digit of our result is 1. 
Result so far: 27259.611
The remainder is 14 after subtracting 126 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 27259.611 with a balance of 0.0014.