Let's divide 10514 by 19
Our goal is to divide 10514 by 19.

Step 1:
When dividing 1 by 19, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 19

Moving on to step 2:
If we divide 10 by 19, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 19

Moving on to step 3:
If we divide 105 by 19, we get 5 and a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Deduct 95 from 105 and we're left with 10.
Bring next digit (1) of the dividend behind the 10 and repeat the process: 101 / 19

Going ahead to step 4:
The number 19 fits into 101 5 times, leaving a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 55.0
Subtracting 95 from 101 leaves us with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 19

On to step 5:
The number 19 fits into 64 3 times, leaving a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 553.0
Deduct 57 from 64 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 6:
The number 19 fits into 70 3 times, leaving a remainder of 13.
Use 3 as the next digit of our solution. 
Result so far: 553.3
If we subtract 57 from 70, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
19 goes into 130 6 times with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 553.36
If we take 114 away from 130, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 8:
19 goes into 160 8 times with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 553.368
If we subtract 152 from 160, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 9:
When dividing 80 by 19, we get 4 with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 553.3684
If we take 76 away from 80, 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.

Advancing to step 10:
When dividing 40 by 19, we get 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 553.36842
The remainder is 2 after subtracting 38 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 11:
20 divided by 19 is 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 553.368421
If we take 19 away from 20, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 12:
If we divide 10 by 19, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 553.368421
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.

On to step 13:
When dividing 100 by 19, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 553.36842105
The remainder is 5 after subtracting 95 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 553.36842105, and the remainder is 5e-09.