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Long Division Steps
Long Division and Remainders


Long division is a little different to short division, but isn’t as difficult as many often perceive it to be.

Here we’ll show 2 examples of solving division sums with long division steps. With one example being long division and remainders.



Long Division Steps,
Long Division and Remainders Examples



1.1

648 ÷ 12 ?

Solution

1)
The first step here in using the long division method is to set the numbers up like we would with a short division sum.

12  648  

For the first bit of division,  12  doesn’t go into  6,  so we put a  0  above in the solution section.
       0
12  648


But now looking at the first two numbers in the dividend together,  12  does go into 64.
Not an exact amount of times, but with “LONG” division, at this stage we ignore any remainders, so  12  goes into  64  five times.

       05
12  648  



2)
Next we multiply the divisor  12  by this  5.     12 × 5 = 60
We then place this number below  64  in the dividend, subtract, then place the result below.

       05
12  648  
   
60
         4


3)
Now the next number in the dividend in brought down alongside the  4.
Here this is  8,  so we will have  48.

       05
12  648  
   
60
         48


This new  48  is now divided by the divisor  12,  and the result is placed appropriately above in the answer.     48 ÷ 12 = 4
        054
12  648  
   
60
          48



4)
Then it’s the same process again, the  4  from the answer is multiplied by the divisor  12.
Then followed by being subtracted from the number sitting above.
4 × 12 = 48


       054
12  648  
   
60
         48
     
48
           0



The result from the last subtraction is  0,  and with no numbers left in the dividend to bring down, the long division sum is complete.
With no remainder in the answer.

648 ÷ 12  =  54





1.2

483 ÷ 15 ?

Solution

1)

15  483  

Firstly,  15  doesn’t go into  4,  so a  0  goes above.
       0
15  483  


Ignoring remainders at this point as usual,  15  does go into  48  three times.
       03
15  483  



2)
Next we multiply the divisor  15  by the  3.     15 × 3 = 45
We then place this number below  48  in the dividend, subtract, then place the result below.

       03
15  483  
   
45
         3



3)  
The next number in the dividend is now brought down and combined with the  3,  giving us  33.

         03
15  483  
     
45
           33


This  33,  again ignoring remainders, can now be divided by the divisor  15,  with the result is placed in the appropriate place above in the answer.
33 ÷ 15 = 2
         032
15  483  
      
45
           33



4)  
Now following same process again, this  2  from the answer is multiplied by the divisor  15.
Followed by being subtracted from the number above again.


         032
15  483  
     
45
           33
       
30
              3



The last result is  3  this time instead of zero.
This is what happens when we have long division and remainders, a non zero last result.
Now as there are no numbers left in the dividend to bring down, the long division steps are complete, with the final  3  being our remainder.

438 ÷ 15  =  32 remainder 3






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