Let's divide 516597 by 34
We want to figure out the number of times 516597 can be divided by 34.

On to step 1:
34 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 34

Advancing to step 2:
When dividing 51 by 34, we get 1 with a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 34 from 51, we get 17.
Take the next digit (6) from the dividend and append it to 17, then repeat: 176 / 34

Step 3:
The number 34 fits into 176 5 times, leaving a remainder of 6.
Put 5 as the next digit of the answer. 
Result so far: 15.0
If we take 170 away from 176, we end up with 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 34

Moving on to step 4:
34 can be fit into 65 1 times, resulting in a remainder of 31.
The next digit of our result is 1. 
Result so far: 151.0
If we subtract 34 from 65, we get 31.
Fetch the next digit (9) from the dividend, attach it to 31 and continue: 319 / 34

Going ahead to step 5:
If we divide 319 by 34, we get 9 and a remainder of 13.
Put 9 as the next digit of the answer. 
Result so far: 1519.0
Deduct 306 from 319 and we're left with 13.
Include the next digit (7) from the dividend after 13, then repeat: 137 / 34

Going ahead to step 6:
When dividing 137 by 34, we get 4 with a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 15194.0
If we subtract 136 from 137, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
When dividing 10 by 34, we get 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 15194.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 8:
100 divided by 34 is 2 with a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 15194.02
The remainder is 32 after subtracting 68 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 9:
34 can be fit into 320 9 times, resulting in a remainder of 14.
Write down 9 as next digit of the result. 
Result so far: 15194.029
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.

Moving on to step 10:
When dividing 140 by 34, we get 4 with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 15194.0294
Subtracting 136 from 140 leaves us 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.

Going ahead to step 11:
If we divide 40 by 34, we get 1 and a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 15194.02941
Deduct 34 from 40 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 12:
If we divide 60 by 34, we get 1 and a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 15194.029411
If we take 34 away from 60, we end up 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.

Our division results in 15194.029411 with a remaining 2.6e-06.