We look at the division of 53874 by 15 
Our goal is to divide 53874 by 15.

On to step 1:
The number 15 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 15

Going ahead to step 2:
When dividing 53 by 15, we get 3 with a remainder of 8.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 45 from 53 and we're left with 8.
Append the next digit (8) from the dividend to 8 and continue with: 88 / 15

Step 3:
When dividing 88 by 15, we get 5 with a remainder of 13.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
If we subtract 75 from 88, we get 13.
Take the next digit (7) from the dividend and append it to 13, then repeat: 137 / 15

Step 4:
15 can be fit into 137 9 times, resulting in a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 359.0
Subtracting 135 from 137 leaves us with 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 15

Step 5:
If we divide 24 by 15, we get 1 and a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 3591.0
Subtracting 15 from 24 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 6:
The number 15 fits into 90 6 times, leaving a remainder of 0.
The next digit of our result is 6. 
Result so far: 3591.6
If we take 90 away from 90, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 7:
When dividing 0 by 15, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 3591.6
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 8:
0 divided by 15 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 3591.6
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 3591.6 with a remainder of 0.0.