We're dividing 509137 by 78 
We want to figure out the number of times 509137 can be divided by 78.

On to step 1:
If we divide 5 by 78, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 78

Advancing to step 2:
78 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Grab the next digit (9) from the dividend, add it to 50, then carry on: 509 / 78

On to step 3:
78 can be fit into 509 6 times, resulting in a remainder of 41.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 468 away from 509, we end up with 41.
Append the next digit (1) from the dividend to 41 and continue with: 411 / 78

Advancing to step 4:
411 divided by 78 is 5 with a remainder of 21.
Write down 5 as next digit of the result. 
Result so far: 65.0
Deduct 390 from 411 and we're left with 21.
Append the next digit (3) from the dividend to 21 and continue with: 213 / 78

Advancing to step 5:
78 can be fit into 213 2 times, resulting in a remainder of 57.
Use 2 as the next digit of our solution. 
Result so far: 652.0
Subtract 156 from 213 to get 57.
Take the next digit (7) from the dividend and append it to 57, then repeat: 577 / 78

Moving on to step 6:
78 can be fit into 577 7 times, resulting in a remainder of 31.
Put 7 as the next digit of the answer. 
Result so far: 6527.0
If we take 546 away from 577, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Going ahead to step 7:
The number 78 fits into 310 3 times, leaving a remainder of 76.
The number 3 becomes the next digit in our result. 
Result so far: 6527.3
If we subtract 234 from 310, we get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 8:
When dividing 760 by 78, we get 9 with a remainder of 58.
The next digit of our result is 9. 
Result so far: 6527.39
Subtract 702 from 760 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 9:
580 divided by 78 is 7 with a remainder of 34.
Put 7 as the next digit of the answer. 
Result so far: 6527.397
Subtracting 546 from 580 leaves us 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.

Advancing to step 10:
If we divide 340 by 78, we get 4 and a remainder of 28.
The number 4 becomes the next digit in our result. 
Result so far: 6527.3974
If we subtract 312 from 340, we get 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:
280 divided by 78 is 3 with a remainder of 46.
The next digit of our result is 3. 
Result so far: 6527.39743
If we subtract 234 from 280, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 12:
78 can be fit into 460 5 times, resulting in a remainder of 70.
The next digit of our result is 5. 
Result so far: 6527.397435
If we subtract 390 from 460, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 13:
If we divide 700 by 78, we get 8 and a remainder of 76.
The number 8 becomes the next digit in our result. 
Result so far: 6527.3974358
If we take 624 away from 700, we end up with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Moving on to step 14:
78 can be fit into 760 9 times, resulting in a remainder of 58.
Put 9 as the next digit of the answer. 
Result so far: 6527.39743589
If we subtract 702 from 760, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The final result is 6527.39743589 with a remainder of 5.8e-08.