34274 ÷ 51 
Our goal is to divide 34274 by 51.

On to step 1:
The number 51 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 51

On to step 2:
The number 51 fits into 34 0 times, leaving a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 34, we end up with 34.
Append the next digit (2) from the dividend to 34 and continue with: 342 / 51

Going ahead to step 3:
51 goes into 342 6 times with a remainder of 36.
Write down 6 as next digit of the result. 
Result so far: 6.0
Deduct 306 from 342 and we're left with 36.
Grab the next digit (7) from the dividend, add it to 36, then carry on: 367 / 51

Moving on to step 4:
51 can be fit into 367 7 times, resulting in a remainder of 10.
The number 7 becomes the next digit in our result. 
Result so far: 67.0
The remainder is 10 after subtracting 357 from 367.
Bring next digit (4) of the dividend behind the 10 and repeat the process: 104 / 51

Let's proceed to step 5:
When dividing 104 by 51, we get 2 with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 672.0
If we subtract 102 from 104, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 6:
When dividing 20 by 51, we get 0 with a remainder of 20.
The next digit of our result is 0. 
Result so far: 672.0
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 7:
When dividing 200 by 51, we get 3 with a remainder of 47.
The number 3 becomes the next digit in our result. 
Result so far: 672.03
If we subtract 153 from 200, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Let's proceed to step 8:
If we divide 470 by 51, we get 9 and a remainder of 11.
The number 9 becomes the next digit in our result. 
Result so far: 672.039
The remainder is 11 after subtracting 459 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 9:
51 goes into 110 2 times with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 672.0392
The remainder is 8 after subtracting 102 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 10:
If we divide 80 by 51, we get 1 and a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 672.03921
Deduct 51 from 80 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 11:
51 can be fit into 290 5 times, resulting in a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 672.039215
If we take 255 away from 290, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 12:
51 goes into 350 6 times with a remainder of 44.
The number 6 becomes the next digit in our result. 
Result so far: 672.0392156
If we subtract 306 from 350, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 13:
When dividing 440 by 51, we get 8 with a remainder of 32.
Use 8 as the next digit of our solution. 
Result so far: 672.03921568
If we subtract 408 from 440, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 672.03921568, and the remainder is 3.2e-08.