501294 ÷ 34 
We're looking to find how many times 34 goes into 501294.

Advancing to step 1:
34 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 34

Advancing to step 2:
The number 34 fits into 50 1 times, leaving a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 16 after subtracting 34 from 50.
Fetch the next digit (1) from the dividend, attach it to 16 and continue: 161 / 34

Advancing to step 3:
161 divided by 34 is 4 with a remainder of 25.
Use 4 as the next digit of our solution. 
Result so far: 14.0
Deduct 136 from 161 and we're left with 25.
Include the next digit (2) from the dividend after 25, then repeat: 252 / 34

Let's proceed to step 4:
34 can be fit into 252 7 times, resulting in a remainder of 14.
Record the quotient 7 as the next digit in the result. 
Result so far: 147.0
If we take 238 away from 252, we end up with 14.
Take the next digit (9) from the dividend and append it to 14, then repeat: 149 / 34

Let's proceed to step 5:
34 can be fit into 149 4 times, resulting in a remainder of 13.
Put 4 as the next digit of the answer. 
Result so far: 1474.0
If we take 136 away from 149, we end up with 13.
Fetch the next digit (4) from the dividend, attach it to 13 and continue: 134 / 34

Going ahead to step 6:
134 divided by 34 is 3 with a remainder of 32.
Put 3 as the next digit of the answer. 
Result so far: 14743.0
The remainder is 32 after subtracting 102 from 134.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
When dividing 320 by 34, we get 9 with a remainder of 14.
The next digit of our result is 9. 
Result so far: 14743.9
Subtract 306 from 320 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.

Advancing to step 8:
34 goes into 140 4 times with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 14743.94
If we take 136 away from 140, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
If we divide 40 by 34, we get 1 and a remainder of 6.
The next digit of our result is 1. 
Result so far: 14743.941
The remainder is 6 after subtracting 34 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 10:
The number 34 fits into 60 1 times, leaving a remainder of 26.
Use 1 as the next digit of our solution. 
Result so far: 14743.9411
Deduct 34 from 60 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The final outcome is 14743.9411, with a leftover of 0.00026.