We're dividing 516583 by 38 
Let's see how many times 38 fits into 516583.

Going ahead to step 1:
When dividing 5 by 38, we get 0 with 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.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 38

Advancing to step 2:
The number 38 fits into 51 1 times, leaving a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 38 from 51, we get 13.
Take the next digit (6) from the dividend and append it to 13, then repeat: 136 / 38

On to step 3:
136 divided by 38 is 3 with a remainder of 22.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 114 from 136, we get 22.
Grab the next digit (5) from the dividend, add it to 22, then carry on: 225 / 38

On to step 4:
38 goes into 225 5 times with a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 135.0
Subtract 190 from 225 to get 35.
Bring next digit (8) of the dividend behind the 35 and repeat the process: 358 / 38

Step 5:
When dividing 358 by 38, we get 9 with a remainder of 16.
Put 9 as the next digit of the answer. 
Result so far: 1359.0
Subtracting 342 from 358 leaves us with 16.
Append the next digit (3) from the dividend to 16 and continue with: 163 / 38

Advancing to step 6:
The number 38 fits into 163 4 times, leaving a remainder of 11.
The number 4 becomes the next digit in our result. 
Result so far: 13594.0
Subtract 152 from 163 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 7:
When dividing 110 by 38, we get 2 with a remainder of 34.
The next digit of our result is 2. 
Result so far: 13594.2
Deduct 76 from 110 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 8:
38 goes into 340 8 times with a remainder of 36.
Put 8 as the next digit of the answer. 
Result so far: 13594.28
Subtracting 304 from 340 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 9:
If we divide 360 by 38, we get 9 and a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 13594.289
If we take 342 away from 360, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 10:
The number 38 fits into 180 4 times, leaving a remainder of 28.
The number 4 becomes the next digit in our result. 
Result so far: 13594.2894
Subtracting 152 from 180 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 11:
38 can be fit into 280 7 times, resulting in a remainder of 14.
The next digit of our result is 7. 
Result so far: 13594.28947
Subtract 266 from 280 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 12:
38 can be fit into 140 3 times, resulting in a remainder of 26.
Use 3 as the next digit of our solution. 
Result so far: 13594.289473
If we take 114 away from 140, 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.

Advancing to step 13:
When dividing 260 by 38, we get 6 with a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 13594.2894736
Deduct 228 from 260 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 14:
38 can be fit into 320 8 times, resulting in a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 13594.28947368
The remainder is 16 after subtracting 304 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final result is 13594.28947368 with a remainder of 1.6e-08.